A feasible method for optimization with orthogonality constraints
Minimization with orthogonality constraints (e.g., ) and/or spherical constraints (e.g., ) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are dif...
Uloženo v:
| Vydáno v: | Mathematical programming Ročník 142; číslo 1-2; s. 397 - 434 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2013
Springer Nature B.V |
| Témata: | |
| ISSN: | 0025-5610, 1436-4646 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Minimization with orthogonality constraints (e.g.,
) and/or spherical constraints (e.g.,
) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. To deal with these difficulties, we apply the Cayley transform—a Crank-Nicolson-like update scheme—to preserve the constraints and based on it, develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics. The efficiency of the proposed algorithms is demonstrated on a variety of test problems. In particular, for the maxcut problem, it exactly solves a decomposition formulation for the SDP relaxation. For polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems, the proposed algorithms run very fast and return solutions no worse than those from their state-of-the-art algorithms. For the quadratic assignment problem, a gap 0.842 % to the best known solution on the largest problem “tai256c” in QAPLIB can be reached in 5 min on a typical laptop. |
|---|---|
| AbstractList | Minimization with orthogonality constraints (e.g., $$X logical or top X = I$$) and/or spherical constraints (e.g., $$\Vert x\Vert _2 = 1$$) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. To deal with these difficulties, we apply the Cayley transform-a Crank-Nicolson-like update scheme-to preserve the constraints and based on it, develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics. The efficiency of the proposed algorithms is demonstrated on a variety of test problems. In particular, for the maxcut problem, it exactly solves a decomposition formulation for the SDP relaxation. For polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems, the proposed algorithms run very fast and return solutions no worse than those from their state-of-the-art algorithms. For the quadratic assignment problem, a gap 0.842 % to the best known solution on the largest problem "tai256ca[euro] in QAPLIB can be reached in 5 min on a typical laptop. Minimization with orthogonality constraints (e.g., ) and/or spherical constraints (e.g., ) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. To deal with these difficulties, we apply the Cayley transform—a Crank-Nicolson-like update scheme—to preserve the constraints and based on it, develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics. The efficiency of the proposed algorithms is demonstrated on a variety of test problems. In particular, for the maxcut problem, it exactly solves a decomposition formulation for the SDP relaxation. For polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems, the proposed algorithms run very fast and return solutions no worse than those from their state-of-the-art algorithms. For the quadratic assignment problem, a gap 0.842 % to the best known solution on the largest problem “tai256c” in QAPLIB can be reached in 5 min on a typical laptop. (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Minimization with orthogonality constraints (e.g., ...) and/or spherical constraints (e.g., ...) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. To deal with these difficulties, we apply the Cayley transform--a Crank-Nicolson-like update scheme--to preserve the constraints and based on it, develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics. The efficiency of the proposed algorithms is demonstrated on a variety of test problems. In particular, for the maxcut problem, it exactly solves a decomposition formulation for the SDP relaxation. For polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems, the proposed algorithms run very fast and return solutions no worse than those from their state-of-the-art algorithms. For the quadratic assignment problem, a gap 0.842 % to the best known solution on the largest problem "tai256c" in QAPLIB can be reached in 5 min on a typical laptop.[PUBLICATION ABSTRACT] |
| Author | Yin, Wotao Wen, Zaiwen |
| Author_xml | – sequence: 1 givenname: Zaiwen surname: Wen fullname: Wen, Zaiwen email: wendouble@gmail.com, zw2109@sjtu.edu.cn organization: Department of Mathematics and Institute of Natural Sciences, Shanghai Jiaotong University – sequence: 2 givenname: Wotao surname: Yin fullname: Yin, Wotao organization: Department of Computational and Applied Mathematics, Rice University |
| BookMark | eNp9kD1PwzAQQC1UJNrCD2CLxMISOMdfzVhVfEmVWGC2HOfSukrjYrtC5deTUAaEBNMNfs93ehMy6nyHhFxSuKEA6jZSoKByoEUOYsZzekLGlDOZc8nliIwBCpELSeGMTGLcAABls9mYzOdZgya6qsVsi2nt66zxIfO75LbuwyTnu-zdpXXmQ_-48p1pXTpk1ncxBeO6FM_JaWPaiBffc0pe7-9eFo_58vnhaTFf5pbxMuUFBSMMNgJEYcsCKa2xrquyrtFKJo0qQWFTFZxVgMbY0jDJrVBCScCKVWxKro__7oJ_22NMeuuixbY1Hfp91JQrITiAZD169Qvd-H3oTx8oXpaFAih7ih4pG3yMARu9C25rwkFT0ENUfYyq-6h6iKpp76hfjnXpq9JQo_3XLI5m7Ld0Kww_bvpT-gSaWI1p |
| CODEN | MHPGA4 |
| CitedBy_id | crossref_primary_10_1109_TCDS_2018_2819826 crossref_primary_10_1109_TCSVT_2016_2628207 crossref_primary_10_1007_s10957_023_02168_6 crossref_primary_10_1145_3469856 crossref_primary_10_1088_2632_2153_ad10ce crossref_primary_10_1109_TCSVT_2018_2842206 crossref_primary_10_1016_j_patrec_2013_05_018 crossref_primary_10_1109_TPAMI_2015_2408359 crossref_primary_10_1007_s10915_024_02495_4 crossref_primary_10_1007_s11432_018_9651_8 crossref_primary_10_1137_130932934 crossref_primary_10_1109_TNNLS_2022_3157711 crossref_primary_10_1371_journal_pone_0249624 crossref_primary_10_1016_j_patcog_2018_06_014 crossref_primary_10_1137_16M1068827 crossref_primary_10_1007_s10915_015_0155_8 crossref_primary_10_1016_j_eswa_2025_127943 crossref_primary_10_1007_s10107_021_01640_3 crossref_primary_10_1007_s10444_021_09880_9 crossref_primary_10_1007_s11042_019_7688_z crossref_primary_10_1007_s10994_016_5577_5 crossref_primary_10_1109_TNNLS_2022_3201881 crossref_primary_10_1016_j_jcp_2018_12_010 crossref_primary_10_1088_1361_651X_aa8345 crossref_primary_10_1137_18M1221679 crossref_primary_10_1155_2023_5872359 crossref_primary_10_1109_TNNLS_2019_2935975 crossref_primary_10_1109_TWC_2017_2707549 crossref_primary_10_1007_s10589_022_00443_2 crossref_primary_10_1109_TIP_2020_3011796 crossref_primary_10_1109_TSP_2013_2296883 crossref_primary_10_1016_j_patcog_2016_11_029 crossref_primary_10_1137_23M1568545 crossref_primary_10_1007_s43670_023_00062_w crossref_primary_10_1016_j_strusafe_2020_102026 crossref_primary_10_1109_TIP_2016_2624140 crossref_primary_10_3390_sym14030462 crossref_primary_10_1016_j_cam_2021_113853 crossref_primary_10_1109_TCSVT_2019_2943902 crossref_primary_10_1007_s40305_020_00322_9 crossref_primary_10_1007_s10107_018_1285_1 crossref_primary_10_1109_TKDE_2018_2858782 crossref_primary_10_1016_j_neucom_2017_10_027 crossref_primary_10_1080_19361610_2019_1581877 crossref_primary_10_1007_s11075_024_01921_w crossref_primary_10_1016_j_engappai_2025_111178 crossref_primary_10_1137_24M1644808 crossref_primary_10_1016_j_knosys_2019_105381 crossref_primary_10_1016_j_jfranklin_2017_07_001 crossref_primary_10_1016_j_ipm_2020_102388 crossref_primary_10_1016_j_sysconle_2023_105549 crossref_primary_10_1007_s00521_017_3220_4 crossref_primary_10_1007_s10915_020_01390_y crossref_primary_10_1007_s11063_021_10483_0 crossref_primary_10_1016_j_jfranklin_2025_107999 crossref_primary_10_1109_ACCESS_2017_2787543 crossref_primary_10_1016_j_cma_2022_115212 crossref_primary_10_1109_TNSRE_2024_3399191 crossref_primary_10_1007_s10915_017_0359_1 crossref_primary_10_1007_s10994_021_06071_x crossref_primary_10_1109_TPAMI_2017_2737538 crossref_primary_10_3390_math11112414 crossref_primary_10_1109_TIP_2017_2745684 crossref_primary_10_1109_TSP_2019_2914884 crossref_primary_10_1109_TNNLS_2017_2690970 crossref_primary_10_1016_j_ins_2025_122183 crossref_primary_10_1007_s11590_018_1319_x crossref_primary_10_1016_j_neunet_2021_07_023 crossref_primary_10_1007_s11425_014_4824_0 crossref_primary_10_1007_s11425_014_4825_z crossref_primary_10_1017_S0962492919000047 crossref_primary_10_1007_s11590_021_01762_9 crossref_primary_10_1007_s11425_017_9096_6 crossref_primary_10_1007_s10479_018_2978_9 crossref_primary_10_3390_e24020188 crossref_primary_10_1109_TMM_2019_2900166 crossref_primary_10_1016_j_cam_2025_117040 crossref_primary_10_1016_j_patcog_2020_107732 crossref_primary_10_1080_10556788_2016_1233973 crossref_primary_10_1109_ACCESS_2024_3368631 crossref_primary_10_1109_TIP_2024_3403493 crossref_primary_10_1088_2632_2153_ac48a2 crossref_primary_10_1016_j_jvcir_2017_10_006 crossref_primary_10_1016_j_patcog_2022_109123 crossref_primary_10_1111_itor_12996 crossref_primary_10_1109_TNSRE_2023_3277867 crossref_primary_10_1007_s10851_020_00961_w crossref_primary_10_1093_comjnl_bxab020 crossref_primary_10_3233_JIFS_200224 crossref_primary_10_1145_3389547 crossref_primary_10_1016_j_jcp_2023_112670 crossref_primary_10_1109_TIP_2021_3120871 crossref_primary_10_1109_TSP_2018_2816568 crossref_primary_10_1016_j_neucom_2019_07_057 crossref_primary_10_1016_j_trc_2024_104538 crossref_primary_10_1109_LWC_2023_3272974 crossref_primary_10_1007_s00211_021_01178_8 crossref_primary_10_1111_biom_13531 crossref_primary_10_1137_13094918X crossref_primary_10_1002_sam_11621 crossref_primary_10_1109_TKDE_2018_2791607 crossref_primary_10_1109_TCYB_2021_3131749 crossref_primary_10_1016_j_csda_2022_107682 crossref_primary_10_1137_140976601 crossref_primary_10_1016_j_knosys_2019_02_036 crossref_primary_10_1016_j_ifacol_2022_11_023 crossref_primary_10_1109_TPAMI_2018_2861871 crossref_primary_10_1186_s13059_025_03576_9 crossref_primary_10_1007_s41237_024_00254_1 crossref_primary_10_1080_10485252_2024_2313137 crossref_primary_10_1016_j_amc_2015_01_044 crossref_primary_10_1016_j_cma_2015_10_015 crossref_primary_10_1090_mcom_3834 crossref_primary_10_1007_s10589_020_00219_6 crossref_primary_10_1016_j_patcog_2020_107645 crossref_primary_10_1016_j_bulsci_2020_102868 crossref_primary_10_1109_TPAMI_2013_240 crossref_primary_10_1186_s12859_022_04826_4 crossref_primary_10_1137_16M1098759 crossref_primary_10_1590_0101_7438_2025_045_00294445 crossref_primary_10_1109_ACCESS_2018_2875270 crossref_primary_10_1007_s11081_024_09921_4 crossref_primary_10_1007_s11222_015_9615_0 crossref_primary_10_1016_j_cam_2022_114915 crossref_primary_10_1109_TII_2023_3316220 crossref_primary_10_1109_TSP_2018_2886151 crossref_primary_10_1007_s10915_024_02476_7 crossref_primary_10_1214_21_AOAS1466 crossref_primary_10_1137_17M115743X crossref_primary_10_1016_j_cam_2025_116716 crossref_primary_10_1016_j_jmva_2022_105140 crossref_primary_10_1109_ACCESS_2023_3349148 crossref_primary_10_1007_s11042_017_5381_7 crossref_primary_10_1007_s10288_020_00445_y crossref_primary_10_1145_3397188 crossref_primary_10_1016_j_neucom_2017_08_070 crossref_primary_10_1007_s11075_014_9924_y crossref_primary_10_1007_s10107_019_01418_8 crossref_primary_10_1007_s10044_018_0753_9 crossref_primary_10_1007_s10107_022_01794_8 crossref_primary_10_1016_j_patcog_2016_07_005 crossref_primary_10_1155_2020_3054764 crossref_primary_10_1126_science_abj6511 crossref_primary_10_1287_ijoc_2024_0701 crossref_primary_10_1109_TWC_2022_3177840 crossref_primary_10_1080_10556788_2017_1415337 crossref_primary_10_1109_MSP_2020_3004034 crossref_primary_10_1007_s10115_017_1069_6 crossref_primary_10_1080_00273171_2019_1677208 crossref_primary_10_1007_s10589_025_00693_w crossref_primary_10_1109_TIM_2024_3443331 crossref_primary_10_1007_s12293_020_00315_4 crossref_primary_10_1109_TAC_2023_3332013 crossref_primary_10_1109_TIP_2024_3354106 crossref_primary_10_1007_s40305_023_00462_8 crossref_primary_10_1080_01621459_2023_2178925 crossref_primary_10_3390_rs12071164 crossref_primary_10_1007_s11075_022_01298_8 crossref_primary_10_1007_s10107_014_0816_7 crossref_primary_10_1007_s11425_016_0301_5 crossref_primary_10_1080_00401706_2021_2008502 crossref_primary_10_1080_10556788_2020_1852236 crossref_primary_10_1109_TKDE_2023_3289882 crossref_primary_10_1007_s11280_017_0497_2 crossref_primary_10_1007_s11390_016_1644_4 crossref_primary_10_1016_j_patcog_2016_11_001 crossref_primary_10_1016_j_jmva_2020_104668 crossref_primary_10_1016_j_sigpro_2020_107738 crossref_primary_10_1137_24M1628578 crossref_primary_10_1109_TSP_2024_3365944 crossref_primary_10_1109_LMWT_2025_3558284 crossref_primary_10_1080_10618600_2023_2205913 crossref_primary_10_1088_1367_2630_ad5e16 crossref_primary_10_1109_TIP_2023_3246793 crossref_primary_10_1137_24M1669153 crossref_primary_10_1007_s10915_017_0412_0 crossref_primary_10_1109_TSP_2022_3182883 crossref_primary_10_1088_2632_2153_adde29 crossref_primary_10_1137_19M1282878 crossref_primary_10_1016_j_dsp_2021_103320 crossref_primary_10_1016_j_patcog_2022_109199 crossref_primary_10_1049_iet_cvi_2015_0322 crossref_primary_10_1007_s10489_025_06563_6 crossref_primary_10_1007_s10898_024_01378_0 crossref_primary_10_1109_JSEN_2018_2884443 crossref_primary_10_1080_00401706_2019_1668854 crossref_primary_10_1109_TPAMI_2019_2933841 crossref_primary_10_1016_j_patcog_2019_01_004 crossref_primary_10_3390_electronics9111888 crossref_primary_10_1016_j_asoc_2020_106773 crossref_primary_10_1007_s10915_018_0757_z crossref_primary_10_1109_TNNLS_2019_2957229 crossref_primary_10_1007_s11042_017_5207_7 crossref_primary_10_1007_s11075_020_01001_9 crossref_primary_10_1109_TEVC_2020_3011829 crossref_primary_10_1002_nla_2363 crossref_primary_10_1134_S1064226922040106 crossref_primary_10_1109_TNNLS_2021_3071127 crossref_primary_10_1109_TIP_2015_2431440 crossref_primary_10_1371_journal_pone_0208494 crossref_primary_10_1137_17M1111176 crossref_primary_10_1016_j_knosys_2022_110244 crossref_primary_10_1007_s11042_017_5272_y crossref_primary_10_1007_s40305_020_00295_9 crossref_primary_10_1093_biomet_asaa036 crossref_primary_10_1137_19M1276170 crossref_primary_10_1109_TNNLS_2023_3301456 crossref_primary_10_1137_15M1048021 crossref_primary_10_1186_s12920_019_0633_1 crossref_primary_10_1186_s12859_018_2188_0 crossref_primary_10_1109_LWC_2024_3376724 crossref_primary_10_1109_TIM_2017_2764298 crossref_primary_10_1007_s10589_017_9925_6 crossref_primary_10_1109_TPAMI_2016_2640292 crossref_primary_10_1093_biomet_asy064 crossref_primary_10_1080_02331934_2022_2142471 crossref_primary_10_1080_10556788_2019_1700257 crossref_primary_10_1007_s10589_022_00433_4 crossref_primary_10_1007_s40314_017_0501_6 crossref_primary_10_1109_TPAMI_2015_2408348 crossref_primary_10_1109_TNNLS_2020_3027526 crossref_primary_10_1109_TCCN_2022_3193403 crossref_primary_10_1109_TPAMI_2021_3092999 crossref_primary_10_1016_j_cam_2021_113814 crossref_primary_10_1109_TNNLS_2014_2376530 crossref_primary_10_1109_TIP_2019_2929421 crossref_primary_10_1137_15M100883X crossref_primary_10_1109_TMM_2020_2978593 crossref_primary_10_1007_s10618_017_0492_3 crossref_primary_10_1137_19M1270872 crossref_primary_10_1007_s10444_021_09855_w crossref_primary_10_1007_s10915_023_02165_x crossref_primary_10_1016_j_patrec_2024_08_011 crossref_primary_10_1109_TSIPN_2025_3536102 crossref_primary_10_1007_s10915_024_02664_5 crossref_primary_10_1007_s00041_020_09761_7 crossref_primary_10_1016_j_cam_2024_116024 crossref_primary_10_1093_imanum_drac084 crossref_primary_10_1109_TIP_2025_3594140 crossref_primary_10_1007_s00211_021_01185_9 crossref_primary_10_1016_j_ifacol_2020_12_020 crossref_primary_10_1109_TNNLS_2017_2671849 crossref_primary_10_1109_TIP_2017_2704661 crossref_primary_10_1534_genetics_120_303153 crossref_primary_10_1080_00207179_2018_1482501 crossref_primary_10_1007_s10589_022_00394_8 crossref_primary_10_1137_19M1291601 crossref_primary_10_1109_ACCESS_2021_3106680 crossref_primary_10_1103_PhysRevB_111_054116 crossref_primary_10_3390_rs14020375 crossref_primary_10_1002_nla_70006 crossref_primary_10_1109_TCYB_2020_3017736 crossref_primary_10_1007_s10915_013_9740_x crossref_primary_10_1109_TSP_2023_3270742 crossref_primary_10_1137_140967994 crossref_primary_10_1137_22M1489447 crossref_primary_10_1109_TCYB_2016_2606441 crossref_primary_10_1007_s11075_023_01701_y crossref_primary_10_1109_TGRS_2019_2930037 crossref_primary_10_1109_ACCESS_2021_3095367 crossref_primary_10_1016_j_spasta_2024_100838 crossref_primary_10_1016_j_neucom_2018_01_088 crossref_primary_10_1016_j_neucom_2023_126237 crossref_primary_10_1007_s10589_024_00595_3 crossref_primary_10_1016_j_dsp_2022_103748 crossref_primary_10_1007_s11063_020_10250_7 crossref_primary_10_1080_00949655_2025_2511926 crossref_primary_10_1007_s40819_024_01689_6 crossref_primary_10_1007_s12021_018_9382_0 crossref_primary_10_1007_s10915_013_9752_6 crossref_primary_10_1038_s42256_020_00265_z crossref_primary_10_1007_s10115_019_01356_z crossref_primary_10_1109_TPAMI_2023_3250241 crossref_primary_10_1111_stan_12262 crossref_primary_10_1137_24M1631122 crossref_primary_10_1109_TKDE_2018_2873378 crossref_primary_10_1007_s11336_017_9575_8 crossref_primary_10_3390_math13152505 crossref_primary_10_1007_s40819_021_01162_8 crossref_primary_10_1016_j_ymssp_2018_11_022 crossref_primary_10_1007_s10107_022_01896_3 crossref_primary_10_1007_s10115_018_1216_8 crossref_primary_10_1007_s10994_023_06369_y crossref_primary_10_1016_j_knosys_2020_106285 crossref_primary_10_1007_s40314_023_02310_0 crossref_primary_10_1109_TAC_2022_3148381 crossref_primary_10_1007_s10898_020_00875_2 crossref_primary_10_1137_23M1561464 crossref_primary_10_1007_s10107_021_01702_6 crossref_primary_10_1371_journal_pcbi_1006056 crossref_primary_10_1007_s10915_022_02025_0 crossref_primary_10_3390_sym16091101 crossref_primary_10_1007_s11263_014_0746_0 crossref_primary_10_1109_JSTSP_2024_3463480 crossref_primary_10_1109_TKDE_2017_2701825 crossref_primary_10_1007_s10801_020_00991_y crossref_primary_10_3150_21_BEJ1402 crossref_primary_10_1093_biomet_asaa087 crossref_primary_10_1137_20M1383720 crossref_primary_10_1016_j_cviu_2022_103415 crossref_primary_10_1007_s40314_020_01184_w crossref_primary_10_1007_s11263_013_0611_6 crossref_primary_10_1002_cpa_21830 crossref_primary_10_1007_s40300_016_0093_8 crossref_primary_10_1016_j_neucom_2024_127899 crossref_primary_10_1109_TASE_2022_3183589 crossref_primary_10_1109_TPAMI_2017_2762295 crossref_primary_10_1137_16M1060224 crossref_primary_10_1093_imanum_draf046 crossref_primary_10_1016_j_patcog_2023_109349 crossref_primary_10_1109_TIP_2015_2479405 crossref_primary_10_1016_j_patrec_2018_04_027 crossref_primary_10_1109_TIP_2017_2740564 crossref_primary_10_1007_s11036_020_01607_2 crossref_primary_10_3390_rs13071372 crossref_primary_10_1016_j_cam_2022_114953 crossref_primary_10_1007_s00521_019_04191_z crossref_primary_10_1111_bmsp_70004 crossref_primary_10_1109_TIP_2019_2912290 crossref_primary_10_1287_moor_2022_1345 crossref_primary_10_1137_20M1354313 crossref_primary_10_1109_TCSVT_2019_2901713 crossref_primary_10_1137_18M122457X crossref_primary_10_1007_s00211_022_01322_y crossref_primary_10_1109_TCYB_2018_2881539 crossref_primary_10_1109_LCSYS_2023_3288229 crossref_primary_10_1109_TIP_2018_2818008 crossref_primary_10_1007_s11222_023_10368_3 crossref_primary_10_1080_10618600_2025_2473936 crossref_primary_10_1088_1741_2552_aa61bb crossref_primary_10_1016_j_neunet_2019_05_009 crossref_primary_10_1088_1751_8121_ad2d6e crossref_primary_10_1007_s10115_019_01334_5 crossref_primary_10_1093_imanum_drx015 crossref_primary_10_1016_j_laa_2021_09_004 crossref_primary_10_1002_qre_2825 crossref_primary_10_1016_j_jmva_2022_105015 crossref_primary_10_1016_j_knosys_2021_106773 crossref_primary_10_1007_s10589_019_00129_2 crossref_primary_10_1016_j_jvcir_2020_102981 crossref_primary_10_1016_j_insmatheco_2023_04_001 crossref_primary_10_1016_j_jcp_2021_110793 crossref_primary_10_1007_s10107_022_01898_1 crossref_primary_10_1080_10618600_2023_2289542 crossref_primary_10_1007_s11590_025_02210_8 crossref_primary_10_3390_s23177486 crossref_primary_10_1016_j_ress_2022_108968 crossref_primary_10_1109_ACCESS_2017_2779562 crossref_primary_10_3390_s20030697 crossref_primary_10_1186_s12864_020_07006_x crossref_primary_10_1007_s10107_014_0765_1 crossref_primary_10_1007_s10589_021_00345_9 crossref_primary_10_1016_j_patrec_2019_06_023 crossref_primary_10_1137_18M121112X crossref_primary_10_1049_el_2013_3159 crossref_primary_10_1080_01621459_2021_1886937 crossref_primary_10_1007_s00500_017_2683_7 crossref_primary_10_1109_TGRS_2024_3389981 crossref_primary_10_1109_TIP_2017_2652730 crossref_primary_10_1007_s11590_021_01801_5 crossref_primary_10_1111_biom_13486 crossref_primary_10_1007_s10846_025_02257_w crossref_primary_10_1007_s10994_021_05987_8 crossref_primary_10_1007_s13160_025_00692_8 crossref_primary_10_1109_TKDE_2023_3321913 crossref_primary_10_1007_s13042_020_01143_1 crossref_primary_10_1016_j_cag_2014_09_016 crossref_primary_10_1371_journal_pone_0215450 crossref_primary_10_1137_140988875 crossref_primary_10_1109_TVT_2019_2893072 crossref_primary_10_1007_s00158_022_03475_8 crossref_primary_10_1109_TKDE_2022_3201955 crossref_primary_10_1007_s00034_013_9706_0 crossref_primary_10_1016_j_cviu_2019_102852 crossref_primary_10_1080_02331934_2016_1246547 crossref_primary_10_1137_20M1348522 crossref_primary_10_1007_s40314_023_02302_0 crossref_primary_10_1007_s10898_021_01104_0 crossref_primary_10_1007_s10915_025_02806_3 crossref_primary_10_1109_TIP_2021_3065843 crossref_primary_10_1109_TIP_2016_2614136 crossref_primary_10_1007_s13042_018_0894_6 crossref_primary_10_1007_s10915_019_00971_w crossref_primary_10_1007_s10589_024_00630_3 crossref_primary_10_1016_j_jcp_2016_10_039 crossref_primary_10_1007_s00362_024_01537_1 crossref_primary_10_1007_s10915_021_01711_9 crossref_primary_10_1145_3052774 crossref_primary_10_1016_j_jvcir_2022_103552 crossref_primary_10_1016_j_ipm_2022_102901 crossref_primary_10_1007_s13042_020_01188_2 crossref_primary_10_1016_j_acha_2023_04_008 crossref_primary_10_1016_j_cpc_2025_109596 crossref_primary_10_1007_s11590_018_1341_z crossref_primary_10_1017_S0956792515000492 crossref_primary_10_1109_TPAMI_2024_3486319 crossref_primary_10_1007_s10589_023_00481_4 crossref_primary_10_1007_s00158_020_02633_0 crossref_primary_10_1109_ACCESS_2020_2978548 crossref_primary_10_1016_j_geomphys_2017_08_011 crossref_primary_10_1109_TSMC_2024_3373612 crossref_primary_10_1137_16M1072929 crossref_primary_10_1007_s11590_015_0977_1 crossref_primary_10_1007_s42081_025_00306_0 crossref_primary_10_1016_j_neunet_2019_12_010 crossref_primary_10_1016_j_neucom_2024_128210 crossref_primary_10_1007_s10589_016_9883_4 crossref_primary_10_1007_s10898_022_01144_0 crossref_primary_10_1007_s10915_020_01173_5 crossref_primary_10_1080_01621459_2020_1862667 crossref_primary_10_1109_TKDE_2020_3045770 crossref_primary_10_1016_j_neucom_2015_12_129 crossref_primary_10_1103_qw96_76b8 crossref_primary_10_1007_s12021_021_09523_w crossref_primary_10_1109_TBME_2017_2688919 crossref_primary_10_1109_LSP_2024_3519459 crossref_primary_10_1016_j_neucom_2022_09_018 crossref_primary_10_1109_TMI_2018_2874964 crossref_primary_10_1007_s11042_022_13903_y crossref_primary_10_3390_agronomy13020515 crossref_primary_10_1109_TIP_2022_3193754 crossref_primary_10_1109_TPAMI_2018_2819978 crossref_primary_10_1007_s10092_022_00471_8 crossref_primary_10_1088_2632_2153_ad444a crossref_primary_10_1109_TBDATA_2017_2742530 crossref_primary_10_1109_TIP_2018_2882155 crossref_primary_10_1016_j_jcp_2021_110622 crossref_primary_10_1109_TIP_2017_2766445 crossref_primary_10_1007_s12532_025_00275_1 crossref_primary_10_1287_moor_2023_1360 crossref_primary_10_1007_s10957_024_02392_8 crossref_primary_10_1016_j_patcog_2017_03_029 crossref_primary_10_1080_00401706_2018_1512901 crossref_primary_10_1137_17M1142478 crossref_primary_10_1137_18M1191506 crossref_primary_10_1016_j_apnum_2022_08_005 crossref_primary_10_1007_s10208_024_09687_2 crossref_primary_10_1016_j_jvcir_2021_103278 crossref_primary_10_1080_17538947_2025_2538212 crossref_primary_10_1109_TPAMI_2021_3136965 crossref_primary_10_1016_j_disopt_2018_10_001 crossref_primary_10_1016_j_automatica_2021_110072 crossref_primary_10_1007_s10898_016_0472_y crossref_primary_10_1109_TNNLS_2017_2763967 crossref_primary_10_1109_LSP_2017_2723084 crossref_primary_10_1109_TNNLS_2016_2514360 crossref_primary_10_1016_j_neucom_2019_06_098 crossref_primary_10_1137_14098973X crossref_primary_10_1007_s11042_018_7007_0 crossref_primary_10_1016_j_sigpro_2016_03_013 crossref_primary_10_1016_j_strusafe_2024_102450 crossref_primary_10_1007_s11075_020_00948_z crossref_primary_10_1137_20M1389571 crossref_primary_10_1007_s10589_024_00568_6 crossref_primary_10_1007_s10208_025_09707_9 crossref_primary_10_1137_20M1321000 crossref_primary_10_1109_TNNLS_2020_3007259 crossref_primary_10_1137_21M1452792 |
| Cites_doi | 10.1137/S0036144504446187 10.1137/S1052623494266365 10.1145/192115.192132 10.1137/070701728 10.1007/978-94-015-8390-9 10.1137/080726926 10.1080/14697680400016182 10.1093/imanum/drn029 10.1137/S1052623497328987 10.1016/j.neucom.2004.11.035 10.1016/j.laa.2009.10.025 10.1137/S0036142901396715 10.1093/biostatistics/kxp008 10.1137/070704575 10.1007/s10107-002-0352-8 10.1137/0724043 10.1007/s10107-004-0559-y 10.1137/S0895479895290954 10.1145/1499096.1499099 10.1016/j.jcp.2006.01.030 10.1093/imanum/8.1.141 10.1137/S1052623497328008 10.1007/s00211-004-0569-y 10.1137/080718206 10.1137/050645506 10.1007/s10107-010-0409-z 10.1093/imanum/22.3.359 10.1109/78.365290 10.1007/s10107-006-0033-0 10.1016/j.laa.2006.11.024 10.1137/S1052623403428208 10.1023/A:1008293323270 10.1016/j.laa.2008.03.016 10.1017/CBO9780511810817 10.1023/A:1022322503301 10.1088/0951-7715/21/9/T03 10.1007/s10208-005-0179-9 10.1063/1.2841077 10.1002/9781118723203 10.1109/TSP.2011.2162324 10.1515/9781400830244 10.1109/CISS.2008.4558487 10.1090/fic/003/09 10.1007/s10107-009-0275-8 10.21314/JOR.2000.023 10.1002/nla.743 10.1109/29.32276 10.2172/834714 |
| ContentType | Journal Article |
| Copyright | Springer and Mathematical Optimization Society 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013 |
| Copyright_xml | – notice: Springer and Mathematical Optimization Society 2012 – notice: Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2013 |
| DBID | AAYXX CITATION 3V. 7SC 7WY 7WZ 7XB 87Z 88I 8AL 8AO 8FD 8FE 8FG 8FK 8FL ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FRNLG F~G GNUQQ HCIFZ JQ2 K60 K6~ K7- L.- L.0 L6V L7M L~C L~D M0C M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1007/s10107-012-0584-1 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) ProQuest Pharma Collection Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Database Suite (ProQuest) Business Premium Collection ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student SciTech Collection (ProQuest) ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database (ProQuest) ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Science Database (ProQuest) Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Business Collection (Alumni Edition) Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete ProQuest One Applied & Life Sciences ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Pharma Collection ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | Computer and Information Systems Abstracts ProQuest Business Collection (Alumni Edition) |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1436-4646 |
| EndPage | 434 |
| ExternalDocumentID | 3123847141 10_1007_s10107_012_0584_1 |
| Genre | Feature |
| GroupedDBID | --K --Z -52 -5D -5G -BR -EM -Y2 -~C -~X .4S .86 .DC .VR 06D 0R~ 0VY 199 1B1 1N0 1OL 1SB 203 28- 29M 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 6TJ 78A 7WY 88I 8AO 8FE 8FG 8FL 8TC 8UJ 8VB 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACNCT ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMOZ AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHQJS AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. B0M BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 DWQXO EAD EAP EBA EBLON EBR EBS EBU ECS EDO EIOEI EJD EMI EMK EPL ESBYG EST ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I-F I09 IAO IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV KOW L6V LAS LLZTM M0C M0N M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQ- NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RIG RNI RNS ROL RPX RPZ RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TH9 TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 XPP YLTOR Z45 Z5O Z7R Z7S Z7X Z7Y Z7Z Z81 Z83 Z86 Z88 Z8M Z8N Z8R Z8T Z8W Z92 ZL0 ZMTXR ZWQNP ~02 ~8M ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG ADXHL AEZWR AFDZB AFFHD AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT PQGLB 7SC 7XB 8AL 8FD 8FK JQ2 L.- L.0 L7M L~C L~D PKEHL PQEST PQUKI PRINS PUEGO Q9U |
| ID | FETCH-LOGICAL-c349t-210a5aef5052c92e11deddb9ddec636a7907efb243b0eaac9a364c575760eb3b3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 635 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000330038100014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0025-5610 |
| IngestDate | Fri Sep 05 09:28:47 EDT 2025 Thu Sep 25 00:39:55 EDT 2025 Sat Nov 29 05:49:02 EST 2025 Tue Nov 18 22:04:24 EST 2025 Fri Feb 21 02:32:42 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1-2 |
| Keywords | Nearest correlation matrix Invariant subspace 65K05 Curvilinear search Maxcut SDP 90C26 Eigenvalue and eigenvector Quadratic assignment problem 90C27 Orthogonality constraint Cayley transformation 90C30 Polynomial optimization Stiefel manifold 90C22 Spherical constraint 49Q99 |
| Language | English |
| License | http://www.springer.com/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c349t-210a5aef5052c92e11deddb9ddec636a7907efb243b0eaac9a364c575760eb3b3 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| PQID | 1449927009 |
| PQPubID | 25307 |
| PageCount | 38 |
| ParticipantIDs | proquest_miscellaneous_1475540063 proquest_journals_1449927009 crossref_primary_10_1007_s10107_012_0584_1 crossref_citationtrail_10_1007_s10107_012_0584_1 springer_journals_10_1007_s10107_012_0584_1 |
| PublicationCentury | 2000 |
| PublicationDate | 20131200 2013-12-00 20131201 |
| PublicationDateYYYYMMDD | 2013-12-01 |
| PublicationDate_xml | – month: 12 year: 2013 text: 20131200 |
| PublicationDecade | 2010 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg – name: Heidelberg |
| PublicationSubtitle | A Publication of the Mathematical Optimization Society |
| PublicationTitle | Mathematical programming |
| PublicationTitleAbbrev | Math. Program |
| PublicationYear | 2013 |
| Publisher | Springer Berlin Heidelberg Springer Nature B.V |
| Publisher_xml | – name: Springer Berlin Heidelberg – name: Springer Nature B.V |
| References | Friedland, Nocedal, Overton (CR21) 1987; 24 He, Li, Zhang (CR27) 2010; 125 CR38 Absil, Mahony, Sepulchre (CR2) 2008 Malick, Povh, Rendl, Wiegele (CR35) 2009; 20 CR34 CR33 CR31 Vese, Osher (CR54) 2002; 40 d’Aspremont, El Ghaoui, Jordan, Lanckriet (CR15) 2007; 49 Nocedal, Wright (CR40) 2006 Burkard, Karisch, Rendl (CR11) 1997; 10 Qi, Gallivan, Absil, Diehl, Glineur, Jarlebring, Michiels (CR43) 2010 Yang, Meza, Lee, Wang (CR60) 2009; 36 Bencteux, Cancés, Hager, Le Bris (CR6) 2010; 47 Raydan (CR44) 1997; 7 Helmberg, Rendl (CR28) 2000; 10 CR9 CR48 Weber, VandeVondele, Hütter, Niklasson (CR57) 2008; 128 Kružík, Prohl (CR32) 2006; 48 Grubišić, Pietersz (CR26) 2007; 422 Zhao, Sun, Toh (CR63) 2010; 20 Schneider, Rohwedder, Neelov, Blauert (CR47) 2009; 27 Wächter, Biegler (CR55) 2006; 106 Burer, Monteiro (CR10) 2003; 95 Simon, Abell (CR49) 2010; 432 Chang, Huang, Yeh (CR13) 2008; 429 Cancès, Le Bris, Lions (CR12) 2008; 21 Roy, Kailath (CR46) 1989; 37 CR19 Absil, Baker, Gallivan (CR1) 2007; 7 Boufounos, Baraniuk (CR8) 2008 CR17 CR16 Helmke, Moore, Brockett (CR29) 1994 Owren, Welfert (CR41) 2000; 40 Rebonato, Jäckel (CR45) 1999; 2 CR56 Nishimori, Akaho (CR39) 2005; 67 Adler, Dedieu, Margulies, Martens, Shub (CR3) 2002; 22 CR51 Edelman, Arias, Smith (CR18) 1999; 20 CR50 Yang (CR59) 1995; 43 Horn, Johnson (CR30) 1985 Sun, Yuan (CR52) 2006 Witten, Tibshirani, Hastie (CR58) 2009; 10 Benson, Ye, Zhang (CR7) 2000; 10 Goldfarb, Wen, Yin (CR23) 2009; 2 Yang, Meza, Wang (CR61) 2006; 217 Nemirovski (CR37) 2007; 109 Udrişte (CR53) 1994 CR25 Golub, Van Loan (CR24) 1996 Pietersz, Groenen (CR42) 2004; 4 CR22 Zhang, Hager (CR62) 2004; 14 Baker, Absil, Gallivan (CR4) 2008; 28 Moré, Thuente (CR36) 1994; 20 Francisco, Martínez, Martínez, Pisnitchenko (CR20) 2011; 10 Barzilai, Borwein (CR5) 1988; 8 Dai, Fletcher (CR14) 2005; 100 C Helmberg (584_CR28) 2000; 10 P Boufounos (584_CR8) 2008 RA Horn (584_CR30) 1985 A d’Aspremont (584_CR15) 2007; 49 A Wächter (584_CR55) 2006; 106 584_CR31 C Udrişte (584_CR53) 1994 584_CR33 584_CR34 GH Golub (584_CR24) 1996 584_CR25 D Goldfarb (584_CR23) 2009; 2 W Sun (584_CR52) 2006 H Zhang (584_CR62) 2004; 14 I Grubišić (584_CR26) 2007; 422 S Burer (584_CR10) 2003; 95 J Nocedal (584_CR40) 2006 R Schneider (584_CR47) 2009; 27 P-A Absil (584_CR2) 2008 584_CR9 G Bencteux (584_CR6) 2010; 47 R Pietersz (584_CR42) 2004; 4 C Yang (584_CR61) 2006; 217 C Yang (584_CR60) 2009; 36 Y-H Dai (584_CR14) 2005; 100 M Raydan (584_CR44) 1997; 7 M Kružík (584_CR32) 2006; 48 J Barzilai (584_CR5) 1988; 8 E Cancès (584_CR12) 2008; 21 584_CR46 584_CR38 RE Burkard (584_CR11) 1997; 10 SJ Benson (584_CR7) 2000; 10 DM Witten (584_CR58) 2009; 10 A Edelman (584_CR18) 1999; 20 JJ Moré (584_CR36) 1994; 20 584_CR51 584_CR50 B Owren (584_CR41) 2000; 40 A Nemirovski (584_CR37) 2007; 109 R Rebonato (584_CR45) 1999; 2 584_CR57 584_CR56 584_CR48 GJ Chang (584_CR13) 2008; 429 Y Nishimori (584_CR39) 2005; 67 B Yang (584_CR59) 1995; 43 S Friedland (584_CR21) 1987; 24 LA Vese (584_CR54) 2002; 40 584_CR20 584_CR22 P-A Absil (584_CR1) 2007; 7 X Zhao (584_CR63) 2010; 20 D Simon (584_CR49) 2010; 432 CG Baker (584_CR4) 2008; 28 584_CR17 584_CR16 584_CR19 U Helmke (584_CR29) 1994 J Malick (584_CR35) 2009; 20 C Qi (584_CR43) 2010 S He (584_CR27) 2010; 125 RL Adler (584_CR3) 2002; 22 |
| References_xml | – ident: CR22 – volume: 48 start-page: 439 year: 2006 end-page: 483 ident: CR32 article-title: Recent developments in the modeling, analysis, and numerics of ferromagnetism publication-title: SIAM Rev. doi: 10.1137/S0036144504446187 – volume: 7 start-page: 26 year: 1997 end-page: 33 ident: CR44 article-title: The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem publication-title: SIAM J. Optim. doi: 10.1137/S1052623494266365 – ident: CR16 – volume: 10 start-page: 555 issue: 3 year: 2011 end-page: 590 ident: CR20 article-title: Inexact restoration method for minimization problems arising in electronic structure calculations publication-title: Comput. Opt. Appl. – volume: 20 start-page: 286 year: 1994 end-page: 307 ident: CR36 article-title: Line search algorithms with guaranteed sufficient decrease publication-title: ACM Trans. Math. Softw. doi: 10.1145/192115.192132 – volume: 47 start-page: 4517 year: 2010 end-page: 4539 ident: CR6 article-title: Analysis of a quadratic programming decomposition algorithm publication-title: SIAM J. Numer. Anal. doi: 10.1137/070701728 – ident: CR51 – year: 1994 ident: CR53 publication-title: Convex Functions and Optimization Methods on Riemannian Manifolds, vol. 297 of Mathematics and its Applications doi: 10.1007/978-94-015-8390-9 – year: 2008 ident: CR2 publication-title: Optimization Algorithms on Matrix Manifolds – volume: 2 start-page: 84 year: 2009 end-page: 109 ident: CR23 article-title: A curvilinear search method for the p-harmonic flow on spheres publication-title: SIAM J. Imaging Sci. doi: 10.1137/080726926 – volume: 4 start-page: 649 year: 2004 end-page: 662 ident: CR42 article-title: Rank reduction of correlation matrices by majorization publication-title: Quant. Finance doi: 10.1080/14697680400016182 – volume: 28 start-page: 665 year: 2008 end-page: 689 ident: CR4 article-title: An implicit trust-region method on Riemannian manifolds publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drn029 – volume: 128 start-page: 084113 issue: 8 year: 2008 ident: CR57 article-title: Direct energy functional minimization under orthogonality constraints publication-title: J. Chem. Phys. – volume: 10 start-page: 673 year: 2000 end-page: 696 ident: CR28 article-title: A spectral bundle method for semidefinite programming publication-title: SIAM J. Optim. doi: 10.1137/S1052623497328987 – volume: 67 start-page: 106 year: 2005 end-page: 135 ident: CR39 article-title: Learning algorithms utilizing quasi-geodesic flows on the stiefel manifold publication-title: Neurocomputing doi: 10.1016/j.neucom.2004.11.035 – volume: 432 start-page: 1152 year: 2010 end-page: 1164 ident: CR49 article-title: A majorization algorithm for constrained correlation matrix approximation publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2009.10.025 – ident: CR25 – volume: 40 start-page: 2085 year: 2002 end-page: 2104 ident: CR54 article-title: Numerical methods for -harmonic flows and applications to image processing publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142901396715 – year: 1994 ident: CR29 article-title: Optimization and dynamical systems publication-title: Communications and Control Engineering Series – ident: CR19 – volume: 10 start-page: 515 year: 2009 end-page: 534 ident: CR58 article-title: A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis publication-title: Biostatistics doi: 10.1093/biostatistics/kxp008 – volume: 20 start-page: 336 year: 2009 end-page: 356 ident: CR35 article-title: Regularization methods for semidefinite programming publication-title: SIAM J. Optim. doi: 10.1137/070704575 – volume: 2 start-page: 17 year: 1999 end-page: 27 ident: CR45 article-title: The most general methodology to create a valid correlation matrix for risk management and option pricing purposes publication-title: J. Risk – ident: CR50 – volume: 27 start-page: 360 year: 2009 end-page: 387 ident: CR47 article-title: Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure publication-title: J. Comput. Math. – volume: 95 start-page: 329 year: 2003 end-page: 357 ident: CR10 article-title: A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization publication-title: Math. Program. doi: 10.1007/s10107-002-0352-8 – volume: 24 start-page: 634 year: 1987 end-page: 667 ident: CR21 article-title: The formulation and analysis of numerical methods for inverse eigenvalue problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/0724043 – volume: 106 start-page: 25 year: 2006 end-page: 57 ident: CR55 article-title: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming publication-title: Math. Program. doi: 10.1007/s10107-004-0559-y – ident: CR9 – volume: 20 start-page: 303 year: 1999 end-page: 353 ident: CR18 article-title: The geometry of algorithms with orthogonality constraints publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479895290954 – volume: 36 start-page: 1 year: 2009 end-page: 35 ident: CR60 article-title: Kssolv-a matlab toolbox for solving the kohn-sham equations publication-title: ACM Trans. Math. Softw. doi: 10.1145/1499096.1499099 – volume: 217 start-page: 709 year: 2006 end-page: 721 ident: CR61 article-title: A constrained optimization algorithm for total energy minimization in electronic structure calculations publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.01.030 – year: 2006 ident: CR40 publication-title: Numerical Optimization. Springer Series in Operations Research and Financial Engineering – volume: 8 start-page: 141 year: 1988 end-page: 148 ident: CR5 article-title: Two-point step size gradient methods publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/8.1.141 – volume: 10 start-page: 443 year: 2000 end-page: 461 ident: CR7 article-title: Solving large-scale sparse semidefinite programs for combinatorial optimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623497328008 – volume: 100 start-page: 21 year: 2005 end-page: 47 ident: CR14 article-title: Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming publication-title: Numer. Math. doi: 10.1007/s00211-004-0569-y – volume: 20 start-page: 1737 year: 2010 end-page: 1765 ident: CR63 article-title: A Newton-CG augmented lagrangian method for semidefinite programming publication-title: SIAM J. Optim. doi: 10.1137/080718206 – volume: 49 start-page: 434 year: 2007 end-page: 448 ident: CR15 article-title: A direct formulation for sparse PCA using semidefinite programming publication-title: SIAM Rev. doi: 10.1137/050645506 – year: 2008 ident: CR8 publication-title: 1-bit Compressive Sensing – ident: CR33 – year: 1996 ident: CR24 publication-title: Matrix Computations – volume: 125 start-page: 353 year: 2010 end-page: 383 ident: CR27 article-title: Approximation algorithms for homogeneous polynomial optimization with quadratic constraints publication-title: Math. Program. doi: 10.1007/s10107-010-0409-z – volume: 22 start-page: 359 year: 2002 end-page: 390 ident: CR3 article-title: Newton’s method on Riemannian manifolds and a geometric model for the human spine publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/22.3.359 – ident: CR56 – volume: 43 start-page: 95 year: 1995 end-page: 107 ident: CR59 article-title: Projection approximation subspace tracking publication-title: IEEE Trans. Signal Process. doi: 10.1109/78.365290 – volume: 109 start-page: 283 year: 2007 end-page: 317 ident: CR37 article-title: Sums of random symmetric matrices and quadratic optimization under orthogonality constraints publication-title: Math. Program. doi: 10.1007/s10107-006-0033-0 – volume: 422 start-page: 629 year: 2007 end-page: 653 ident: CR26 article-title: Efficient rank reduction of correlation matrices publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2006.11.024 – volume: 14 start-page: 1043 year: 2004 end-page: 1056 ident: CR62 article-title: A nonmonotone line search technique and its application to unconstrained optimization publication-title: SIAM J. Optim. doi: 10.1137/S1052623403428208 – volume: 10 start-page: 391 year: 1997 end-page: 403 ident: CR11 article-title: QAPLIB: a quadratic assignment problem library publication-title: J. Global Optim. doi: 10.1023/A:1008293323270 – ident: CR48 – volume: 37 start-page: 984 issue: 7 year: 1989 end-page: 995 ident: CR46 article-title: Esprit—estimation of signal parameters via rotational invariance techniques publication-title: IEEE Trans. Acoust, Speech, Signal Process. – volume: 429 start-page: 601 year: 2008 end-page: 605 ident: CR13 article-title: On the rank of a cograph publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2008.03.016 – ident: CR38 – ident: CR17 – ident: CR31 – year: 1985 ident: CR30 publication-title: Matrix Analysis doi: 10.1017/CBO9780511810817 – year: 2010 ident: CR43 article-title: Riemannian BFGS algorithm with applications publication-title: Recent Advances in Optimization and its Applications in Engineering – volume: 40 start-page: 121 year: 2000 end-page: 145 ident: CR41 article-title: The Newton iteration on Lie groups publication-title: BIT doi: 10.1023/A:1022322503301 – year: 2006 ident: CR52 publication-title: Optimization Theory and Methods, vol. 1 of Springer Optimization and its Applications – ident: CR34 – volume: 21 start-page: T165 year: 2008 end-page: T176 ident: CR12 article-title: Molecular simulation and related topics: some open mathematical problems publication-title: Nonlinearity doi: 10.1088/0951-7715/21/9/T03 – volume: 7 start-page: 303 year: 2007 end-page: 330 ident: CR1 article-title: Trust-region methods on Riemannian manifolds publication-title: Found. Comput. Math. doi: 10.1007/s10208-005-0179-9 – ident: 584_CR57 doi: 10.1063/1.2841077 – volume: 24 start-page: 634 year: 1987 ident: 584_CR21 publication-title: SIAM J. Numer. Anal. doi: 10.1137/0724043 – volume: 10 start-page: 443 year: 2000 ident: 584_CR7 publication-title: SIAM J. Optim. doi: 10.1137/S1052623497328008 – volume: 10 start-page: 515 year: 2009 ident: 584_CR58 publication-title: Biostatistics doi: 10.1093/biostatistics/kxp008 – volume: 40 start-page: 121 year: 2000 ident: 584_CR41 publication-title: BIT doi: 10.1023/A:1022322503301 – volume: 4 start-page: 649 year: 2004 ident: 584_CR42 publication-title: Quant. Finance doi: 10.1080/14697680400016182 – ident: 584_CR38 – volume: 429 start-page: 601 year: 2008 ident: 584_CR13 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2008.03.016 – ident: 584_CR34 – ident: 584_CR50 – volume: 67 start-page: 106 year: 2005 ident: 584_CR39 publication-title: Neurocomputing doi: 10.1016/j.neucom.2004.11.035 – volume: 106 start-page: 25 year: 2006 ident: 584_CR55 publication-title: Math. Program. doi: 10.1007/s10107-004-0559-y – ident: 584_CR19 doi: 10.1002/9781118723203 – volume: 10 start-page: 391 year: 1997 ident: 584_CR11 publication-title: J. Global Optim. doi: 10.1023/A:1008293323270 – volume: 125 start-page: 353 year: 2010 ident: 584_CR27 publication-title: Math. Program. doi: 10.1007/s10107-010-0409-z – volume: 100 start-page: 21 year: 2005 ident: 584_CR14 publication-title: Numer. Math. doi: 10.1007/s00211-004-0569-y – volume: 2 start-page: 84 year: 2009 ident: 584_CR23 publication-title: SIAM J. Imaging Sci. doi: 10.1137/080726926 – ident: 584_CR48 – volume: 217 start-page: 709 year: 2006 ident: 584_CR61 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.01.030 – ident: 584_CR33 doi: 10.1109/TSP.2011.2162324 – volume-title: Optimization Algorithms on Matrix Manifolds year: 2008 ident: 584_CR2 doi: 10.1515/9781400830244 – volume-title: 1-bit Compressive Sensing year: 2008 ident: 584_CR8 doi: 10.1109/CISS.2008.4558487 – volume: 109 start-page: 283 year: 2007 ident: 584_CR37 publication-title: Math. Program. doi: 10.1007/s10107-006-0033-0 – ident: 584_CR22 – volume: 48 start-page: 439 year: 2006 ident: 584_CR32 publication-title: SIAM Rev. doi: 10.1137/S0036144504446187 – volume: 47 start-page: 4517 year: 2010 ident: 584_CR6 publication-title: SIAM J. Numer. Anal. doi: 10.1137/070701728 – volume: 422 start-page: 629 year: 2007 ident: 584_CR26 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2006.11.024 – ident: 584_CR51 doi: 10.1090/fic/003/09 – volume: 8 start-page: 141 year: 1988 ident: 584_CR5 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/8.1.141 – ident: 584_CR9 – volume: 49 start-page: 434 year: 2007 ident: 584_CR15 publication-title: SIAM Rev. doi: 10.1137/050645506 – ident: 584_CR16 – volume-title: Matrix Analysis year: 1985 ident: 584_CR30 doi: 10.1017/CBO9780511810817 – volume: 20 start-page: 336 year: 2009 ident: 584_CR35 publication-title: SIAM J. Optim. doi: 10.1137/070704575 – volume: 432 start-page: 1152 year: 2010 ident: 584_CR49 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2009.10.025 – ident: 584_CR25 doi: 10.1007/s10107-009-0275-8 – volume: 20 start-page: 1737 year: 2010 ident: 584_CR63 publication-title: SIAM J. Optim. doi: 10.1137/080718206 – volume: 28 start-page: 665 year: 2008 ident: 584_CR4 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drn029 – volume: 20 start-page: 286 year: 1994 ident: 584_CR36 publication-title: ACM Trans. Math. Softw. doi: 10.1145/192115.192132 – volume-title: Numerical Optimization. Springer Series in Operations Research and Financial Engineering year: 2006 ident: 584_CR40 – volume-title: Convex Functions and Optimization Methods on Riemannian Manifolds, vol. 297 of Mathematics and its Applications year: 1994 ident: 584_CR53 doi: 10.1007/978-94-015-8390-9 – volume: 43 start-page: 95 year: 1995 ident: 584_CR59 publication-title: IEEE Trans. Signal Process. doi: 10.1109/78.365290 – volume: 2 start-page: 17 year: 1999 ident: 584_CR45 publication-title: J. Risk doi: 10.21314/JOR.2000.023 – volume-title: Optimization Theory and Methods, vol. 1 of Springer Optimization and its Applications year: 2006 ident: 584_CR52 – volume: 22 start-page: 359 year: 2002 ident: 584_CR3 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/22.3.359 – volume: 7 start-page: 303 year: 2007 ident: 584_CR1 publication-title: Found. Comput. Math. doi: 10.1007/s10208-005-0179-9 – volume: 21 start-page: T165 year: 2008 ident: 584_CR12 publication-title: Nonlinearity doi: 10.1088/0951-7715/21/9/T03 – volume: 10 start-page: 673 year: 2000 ident: 584_CR28 publication-title: SIAM J. Optim. doi: 10.1137/S1052623497328987 – volume: 20 start-page: 303 year: 1999 ident: 584_CR18 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479895290954 – ident: 584_CR56 – volume-title: Recent Advances in Optimization and its Applications in Engineering year: 2010 ident: 584_CR43 – ident: 584_CR31 doi: 10.1002/nla.743 – ident: 584_CR46 doi: 10.1109/29.32276 – ident: 584_CR17 doi: 10.2172/834714 – volume-title: Communications and Control Engineering Series year: 1994 ident: 584_CR29 – volume-title: Matrix Computations year: 1996 ident: 584_CR24 – volume: 7 start-page: 26 year: 1997 ident: 584_CR44 publication-title: SIAM J. Optim. doi: 10.1137/S1052623494266365 – ident: 584_CR20 – volume: 14 start-page: 1043 year: 2004 ident: 584_CR62 publication-title: SIAM J. Optim. doi: 10.1137/S1052623403428208 – volume: 40 start-page: 2085 year: 2002 ident: 584_CR54 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142901396715 – volume: 27 start-page: 360 year: 2009 ident: 584_CR47 publication-title: J. Comput. Math. – volume: 95 start-page: 329 year: 2003 ident: 584_CR10 publication-title: Math. Program. doi: 10.1007/s10107-002-0352-8 – volume: 36 start-page: 1 year: 2009 ident: 584_CR60 publication-title: ACM Trans. Math. Softw. doi: 10.1145/1499096.1499099 |
| SSID | ssj0001388 |
| Score | 2.60137 |
| Snippet | Minimization with orthogonality constraints (e.g.,
) and/or spherical constraints (e.g.,
) has wide applications in polynomial optimization, combinatorial... (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) Minimization with orthogonality constraints (e.g., ...) and/or spherical... Minimization with orthogonality constraints (e.g., $$X logical or top X = I$$) and/or spherical constraints (e.g., $$\Vert x\Vert _2 = 1$$) has wide... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 397 |
| SubjectTerms | Algorithms Analysis Applied mathematics Assignment problem Calculus of Variations and Optimal Control; Optimization Combinatorics Eigenvalues Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Partial differential equations Polynomials Studies Theoretical Topological manifolds |
| SummonAdditionalLinks | – databaseName: Science Database (ProQuest) dbid: M2P link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8QwEB58HfTgW1xfRPCkBJs22zQnWUTxsosHBW8lSVMRdLva1d_vTDfdVUEvHkvTJmQmky8zk_kATmRqtfEu5rH0XS5L1eVZKS1H7SkyEVnUqawhm1CDQfbwoG-Dw60OaZWtTWwMdVE58pGfI_DXmqKk-mL0yok1iqKrgUJjHhYR2QhK6erHt1NLLJIsaylbCSe0Uc3J1TnRJF3GPMI9mIvv-9IMbP6IjzbbzvXafwe8DqsBcLLeREM2YM4PN2HlSxlCfOpPa7fWW9DrsdIbXCnPnk34pRkCW1ahbXkJlzYZeW8ZRXyqx4DkmSOgSXwT43ob7q-v7i5veCBa4C6Reszx2Ge6xpdEaud07IUofFFYjabPpUlqFJ6gfWljmdjIG-O0SVLpEOipNMLDuE12YGFYDf0usCJ2mRXYTHdLqWSptTOFliox1ipV6A5E7TTnLlQhp8E957P6ySSZHCWTk2Ry0YHT6SejSQmOvxoftNLIw2qs85koOnA8fY3riIIjZuird2qjEFkRYuvAWSvzL7_4rcO9vzvch-WYCDSaBJgDWBi_vftDWHIf46f67ahR10_Rgu_q priority: 102 providerName: ProQuest |
| Title | A feasible method for optimization with orthogonality constraints |
| URI | https://link.springer.com/article/10.1007/s10107-012-0584-1 https://www.proquest.com/docview/1449927009 https://www.proquest.com/docview/1475540063 |
| Volume | 142 |
| WOSCitedRecordID | wos000330038100014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: ABI/INFORM Collection customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: 7WY dateStart: 20011001 isFulltext: true titleUrlDefault: https://www.proquest.com/abicomplete providerName: ProQuest – providerCode: PRVPQU databaseName: ABI/INFORM Global customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M0C dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/abiglobal providerName: ProQuest – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: P5Z dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: K7- dateStart: 20011001 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M7S dateStart: 20011001 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: BENPR dateStart: 20011001 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database (ProQuest) customDbUrl: eissn: 1436-4646 dateEnd: 20171231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: M2P dateStart: 20011001 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest – providerCode: PRVAVX databaseName: Springer Online Journals customDbUrl: eissn: 1436-4646 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001388 issn: 0025-5610 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB58HfTgW1wfSwRPSqCPtGmOqyiCuCy-9VKSNBVh3RW7-vud6bbrKiroJRA6TcNkMvNNJ5kB2BWxUdrZgAfCRVzkMuJJLgxH6ckS3zMoU0lZbEK228ntrepU97iL-rR7HZIsNfXYZTe_PCYZcA-tJkeXZxqtXUL1Gs4vrkfq1w-TpK7TSuCgDmV-N8RnY_SBML8ERUtbc7zwr1kuwnwFLVlrKAtLMOF6yzA3lnAQe2ejLK3FCrRaLHca90TXsWElaYYQlvVRizxV1zMZ_adlFNvpP1SYnVmClFRZYlCswtXx0eXhCa9KKnAbCjXg6ODpSLucytdZFTjfz1yWGYVKzsZhrCX6yi43gQiN57S2SoexsAjpZOyh223CNZjq9XtuHVgW2MT4SKaiXEiRK2V1poQMtTFSZqoBXs3b1Fb5xmly3fQjUzLxKkVepcSr1G_A3uiV52Gyjd-It-oFS6t9V6Ajgx4cxdLx8zujx7hjKAyie67_SjQSMRRhswbs14s4NsRPH9z4E_UmzAZUOaM8-bIFU4OXV7cNM_Zt8Fi8NGFS3tw1YfrgqN05x96p5NieeYfUBh1q5QW2nei-WYr3O-eS7F8 |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1NT9wwEB1RQCocaKFFLNDWleiFymrieOP4UFUrKAIBKw4gcQu24yAk2ABZQPwpfiMz-diFSnDj0GMUx04y4_Ebz3gewJqMrTbeCS6k73KZqy5Pcmk5ak-WhIFFnUoqsgnV7yfHx_pgAh7aszCUVtnaxMpQZ4WjPfJfCPy1piip_nN5xYk1iqKrLYVGrRa7_v4OXbby984myveHEFt_Dze2ecMqwF0k9ZCjj2O6xufE4Oa08GGY-SyzGue5i6PYKHQXfW6FjGzgjXHaRLF0iGpUHKDnaSPs9x1MSaosRqmC4mBk-cMoSVqKWMIlbRS1PqoXVkmegge45vPw-To4Brf_xGOrZW7rw__2gz7CXAOoWa-eAfMw4QcLMPukzCJe7Y9q05afoNdjuTdoCc49q_mzGQJ3VqDtvGgOpTLanWYU0SpOG0-FOQLSxKcxLD_D0Zt80SJMDoqBXwKWCZfYEJvpbi6VzLV2JtNSRcZapTLdgaAVa-qaKuv0cufpuD40aUKKmpCSJqRhB9ZHj1zWJUZea7zaSj9trE2ZjkXfge-j22gnKPhjBr64oTYKkSMh0g78bHXsSRcvDbj8-oDf4P324f5eurfT312BGUFkIVWyzypMDq9v_BeYdrfDs_L6azVVGJy8teo9ArGlTy0 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3dS8MwEA8yRfTBb3F-RvBJCetH1jSPQx2KOgZ-sLeSpKkIsx22-vd717VzigriY-k1CZdL8rve5X6EHPFAS2WNxzxu24wnos3ChGsG1hOHrqPBpsKSbEL0euFgIPsVz2leZ7vXIcnxnQas0pQWrVGctKYuvrllyqTHHDhBGbg_sxzz6NFdv32YbMWuH4Y1ZysChTqs-V0Tnw-mD7T5JUBanjvd5X-PeIUsVZCTdsY2skpmbLpGFqcKEcLTzaR6a75OOh2aWAVrZWjpmGGaArSlGewuz9W1TYr_bynGfLLHCstTg1ATGSeKfIPcd8_vTi9YRbXAjM9lwcDxU21lE6S1M9KzrhvbONYSNj8T-IES4EPbRHvc145VykjlB9wA1BOBA-649jdJI81Su0Vo7JlQuyAm2wkXPJHSqFhy4SuthYhlkzi1niNT1SHHwQ2jjwrKqKsIdBWhriK3SY4nn4zGRTh-E96tJy-q1mMODg54dhhjh-4PJ69hJWF4RKU2e0UZAdgKMVuTnNQTOtXETx1u_0n6gMz3z7rR9WXvaocseEiuUSbH7JJG8fJq98iceSue8pf90pLfAeAp8Ow |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+feasible+method+for+optimization+with+orthogonality+constraints&rft.jtitle=Mathematical+programming&rft.au=Wen%2C+Zaiwen&rft.au=Yin%2C+Wotao&rft.date=2013-12-01&rft.pub=Springer+Berlin+Heidelberg&rft.issn=0025-5610&rft.eissn=1436-4646&rft.volume=142&rft.issue=1-2&rft.spage=397&rft.epage=434&rft_id=info:doi/10.1007%2Fs10107-012-0584-1&rft.externalDocID=10_1007_s10107_012_0584_1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0025-5610&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0025-5610&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0025-5610&client=summon |