Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem
In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computat...
Gespeichert in:
| Veröffentlicht in: | Acta Mathematicae Applicatae Sinica Jg. 30; H. 3; S. 707 - 720 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2014
|
| Schlagworte: | |
| ISSN: | 0168-9673, 1618-3932 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved. |
|---|---|
| AbstractList | In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved. |
| Author | Cong-ying HAN Fang-ying ZHENG Tian-de GUO Guo-ping HE |
| AuthorAffiliation | School of Mathematical Sciences, University of the Chinese Academy of Sciences, No.19（A）, Yuquan Road, Shijingshan District, Beijing 100049, China Department of Mathematical Science, Zhejiang Sci-Tech University, Hangzhou 310018, China College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao266510, China |
| Author_xml | – sequence: 1 givenname: Cong-ying surname: Han fullname: Han, Cong-ying email: hancy@ucas.ac.cn organization: School of Mathematical Sciences, University of the Chinese Academy of Sciences – sequence: 2 givenname: Fang-ying surname: Zheng fullname: Zheng, Fang-ying organization: Department of Mathematical Science, Zhejiang Sci-Tech University – sequence: 3 givenname: Tian-de surname: Guo fullname: Guo, Tian-de organization: School of Mathematical Sciences, University of the Chinese Academy of Sciences – sequence: 4 givenname: Guo-ping surname: He fullname: He, Guo-ping organization: College of Information Science and Engineering, Shandong University of Science and Technology |
| BookMark | eNp9kLtOwzAUhi1UJNrCA7CFBzD4EtvxWFXcpFR0gNkyiZ26cmyww1CenpRWDAydjo50vvNfZmASYjAAXGN0ixESdxkjwhhEmEJEEYLyDEwxxxWkkpIJmCLMKyi5oBdglvMWISwoF1OwWuukvTe-WPguJjds-lzYmIpap87A3GhvitoFo5PfFcsY8pD0uLbFygXXu289uBiKdYrv3vSX4Nxqn83Vcc7B28P96_IJ1i-Pz8tFDRuKywFKInjLLGsbYTVtBSdECMIsNoQZzXkjqSCVaJHlumorWpWUlpJwUiJbSWLpHIjD3ybFnJOxqnHDr5O9O68wUvtW1KEVNbai9q0oOZL4H_mRXK_T7iRDDkweb0NnktrGrxTGgCehm6PQJobuc-T-lBgiJWZjph8ODIEU |
| CitedBy_id | crossref_primary_10_1186_s13662_018_1908_0 crossref_primary_10_1007_s10589_017_9931_8 crossref_primary_10_1109_TETCI_2018_2881490 crossref_primary_10_1016_j_cam_2018_10_035 crossref_primary_10_1155_2019_4861708 crossref_primary_10_1080_19439962_2018_1564946 crossref_primary_10_1186_s13638_018_1077_6 crossref_primary_10_1109_ACCESS_2018_2877428 crossref_primary_10_1155_2019_8709042 crossref_primary_10_1016_j_adhoc_2020_102094 crossref_primary_10_1155_2019_3087949 crossref_primary_10_1007_s00521_019_04214_9 crossref_primary_10_1155_2017_1564642 crossref_primary_10_1186_s13638_017_0895_2 crossref_primary_10_1016_j_adhoc_2019_101969 crossref_primary_10_1080_01630563_2018_1483948 crossref_primary_10_1155_2018_6538610 crossref_primary_10_1515_math_2019_0011 crossref_primary_10_1109_ACCESS_2018_2879813 crossref_primary_10_1186_s13638_017_0968_2 crossref_primary_10_1109_ACCESS_2018_2808473 crossref_primary_10_1080_00207160_2018_1506108 crossref_primary_10_1186_s13638_019_1379_3 |
| Cites_doi | 10.1016/j.amc.2009.01.081 10.1023/A:1008618009738 10.1023/A:1008629511432 10.1137/0326019 10.1023/A:1008731209637 10.1137/S1052623496309879 10.1137/0804018 10.1023/A:1014890403681 10.1137/S1052623495293949 10.1080/02331939208843795 10.1137/0804047 |
| ContentType | Journal Article |
| Copyright | Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014 |
| Copyright_xml | – notice: Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014 |
| DBID | 2RA 92L CQIGP ~WA AAYXX CITATION |
| DOI | 10.1007/s10255-013-0300-9 |
| DatabaseName | 维普期刊资源整合服务平台 中文科技期刊数据库-CALIS站点 维普中文期刊数据库 中文科技期刊数据库- 镜像站点 CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| DocumentTitleAlternate | Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem |
| EISSN | 1618-3932 |
| EndPage | 720 |
| ExternalDocumentID | 10_1007_s10255_013_0300_9 50241543 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 1N0 1SB 2.D 23M 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2RA 2VQ 2~H 30V 4.4 406 408 40D 40E 5GY 5QI 5VR 5VS 6NX 8TC 8UJ 92L 95- 95. 95~ 96X AAAVM AABHQ AABYN AAFGU AAHNG AAIAL AAJKR AANZL AARHV AARTL AATNV AATVU AAUYE AAWCG AAYFA AAYIU AAYQN AAYTO ABBBX ABDZT ABECU ABFGW ABFTV ABHLI ABHQN ABJOX ABKAS ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBMV ACBRV ACBXY ACBYP ACGFS ACHSB ACHXU ACIGE ACIPQ ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACTTH ACVWB ACWMK ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADMDM ADOXG ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEEQQ AEFIE AEFTE AEGAL AEGNC AEJHL AEJRE AEKMD AEOHA AEPOP AEPYU AESKC AESTI AETLH AEVLU AEVTX AEXYK AFEXP AFGCZ AFLOW AFMKY AFNRJ AFQWF AFUIB AFWTZ AFZKB AGAYW AGDGC AGGBP AGGDS AGJBK AGMZJ AGPAZ AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AIMYW AITGF AJBLW AJDOV AJRNO AKQUC ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ AXYYD B-. BA0 BAPOH BBWZM BDATZ BGNMA CAG CCEZO CCVFK CHBEP COF CQIGP CS3 CSCUP CW9 DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI EJD ESBYG F5P FA0 FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 HF~ HG6 HMJXF HRMNR HVGLF HZ~ IHE IJ- IKXTQ IWAJR IXD I~X I~Z J-C JBSCW JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J P19 P2P P9R PF0 PT4 PT5 QOK QOS R4E R89 R9I REI RHV RNI ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCL SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TSG TSK TSV TUC U2A UG4 UNUBA UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR ZMTXR ZWQNP ~A9 ~EX ~WA -SA -S~ 5XA 5XB AACDK AAJBT AASML AAXDM AAYZH ABAKF ABQSL ACDTI ACPIV AEFQL AEMSY AGQEE AGRTI AIGIU BSONS CAJEA H13 Q-- U1G U5K AAPKM AAYXX ABBRH ABDBE ABRTQ ADHKG AFDZB AFOHR AGQPQ AHPBZ ATHPR AYFIA CITATION TGP |
| ID | FETCH-LOGICAL-c314t-9276d5f5dc7fa3d76227725f1e25ea66c937287d0f6a8d8384334926240f892f3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 24 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000341462800014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0168-9673 |
| IngestDate | Sat Nov 29 06:47:20 EST 2025 Tue Nov 18 20:04:15 EST 2025 Fri Feb 21 02:33:57 EST 2025 Wed Feb 14 10:35:28 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | large-scale minimization constrained convex optimization 90C30 90C52 nonlinear programming parallel algorithm 90C06 49M37 65Y05 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c314t-9276d5f5dc7fa3d76227725f1e25ea66c937287d0f6a8d8384334926240f892f3 |
| Notes | In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient function, the new algorithm uses the reduced gradients to construct the PVD directions in parallel computation, which can greatly reduce the computation amount each iteration and is closer to practical applications for solve large-scale nonlinear programming. Moreover, based on an active set computed by the coordinate rotation at each iteration, a feasible descent direction can be easily obtained by the extended reduced gradient method. The direction is then used as the PVD direction and a new PVD algorithm is proposed for the general linearly constrained optimization. And the global convergence is also proved. 11-2041/O1 nonlinear programming; large-scale minimization; parallel algorithm; constrained convex opti-mization |
| PageCount | 14 |
| ParticipantIDs | crossref_citationtrail_10_1007_s10255_013_0300_9 crossref_primary_10_1007_s10255_013_0300_9 springer_journals_10_1007_s10255_013_0300_9 chongqing_primary_50241543 |
| PublicationCentury | 2000 |
| PublicationDate | 20140700 |
| PublicationDateYYYYMMDD | 2014-07-01 |
| PublicationDate_xml | – month: 7 year: 2014 text: 20140700 |
| PublicationDecade | 2010 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg |
| PublicationSubtitle | English Series |
| PublicationTitle | Acta Mathematicae Applicatae Sinica |
| PublicationTitleAbbrev | Acta Math. Appl. Sin. Engl. Ser |
| PublicationTitleAlternate | Acta Mathematicae Applicatae Sinica |
| PublicationYear | 2014 |
| Publisher | Springer Berlin Heidelberg |
| Publisher_xml | – name: Springer Berlin Heidelberg |
| References | Jian (CR9) 1993; 1 Solodov (CR13) 1998; 8 Han, Lou (CR18) 1988; 26 Pang, Xia (CR10) 2003; 29 Fukushima (CR14) 1998; 8 Sagastizábal, Solodov (CR4) 2002; 22 Ferris, Mangasarian (CR11) 1994; 4 CR17 Fischer (CR1) 1992; 24 CR15 Yamakawa, Fukushima (CR7) 1999; 13 Flecher (CR16) 1987 Friendlander, Martínez, Santos (CR2) 1994; 4 Ortega (CR8) 1972 Solodov (CR12) 1997; 7 Han, Wang, He (CR5) 2009; 211 Liu, Tseng (CR3) 2000; 17 Bertsekas, Tsitsiklis (CR6) 1989 JB Jian (300_CR9) 1993; 1 DP Bertsekas (300_CR6) 1989 CY Han (300_CR5) 2009; 211 MV Solodov (300_CR13) 1998; 8 R Flecher (300_CR16) 1987 M Fukushima (300_CR14) 1998; 8 E Yamakawa (300_CR7) 1999; 13 A Friendlander (300_CR2) 1994; 4 CA Sagastizábal (300_CR4) 2002; 22 LP Pang (300_CR10) 2003; 29 MC Ferris (300_CR11) 1994; 4 300_CR17 MV Solodov (300_CR12) 1997; 7 CS Liu (300_CR3) 2000; 17 300_CR15 JM Ortega (300_CR8) 1972 A Fischer (300_CR1) 1992; 24 SP Han (300_CR18) 1988; 26 |
| References_xml | – year: 1972 ident: CR8 publication-title: Numerical Analysis – volume: 1 start-page: 70 year: 1993 end-page: 78 ident: CR9 article-title: An extension of reduced gradient method for linearly constrained programmings publication-title: Mathematics in Economics – volume: 211 start-page: 434 year: 2009 end-page: 441 ident: CR5 article-title: On the convergence of asynchronous parallel algorithm for large-scale linearly constrained minimization problem publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2009.01.081 – volume: 7 start-page: 165 year: 1997 end-page: 182 ident: CR12 article-title: New inexact parallel variable distribution algorithms publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008618009738 – volume: 13 start-page: 1 year: 1999 end-page: 22 ident: CR7 article-title: Testing parallel variable transformation publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008629511432 – volume: 26 start-page: 346 year: 1988 end-page: 355 ident: CR18 article-title: A parallel algorithm for a class of convex programs publication-title: SIAM J. Control Optim. doi: 10.1137/0326019 – volume: 17 start-page: 85 year: 2000 end-page: 107 ident: CR3 article-title: Parallel synchronous and asynchronous space-decomposition algorithms for largescale minimization publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008731209637 – ident: CR15 – year: 1989 ident: CR6 publication-title: Parallel and Distributed Computation: Numerical Methods – volume: 8 start-page: 658 issue: 4 year: 1998 end-page: 672 ident: CR14 article-title: Parallel variable transformation in unconstrained optimization publication-title: SIAM J. Optimization doi: 10.1137/S1052623496309879 – volume: 4 start-page: 331 issue: 2 year: 1994 end-page: 339 ident: CR2 article-title: On the resolution of linearly constrained convex minimization problems publication-title: SIAM J. Optimization doi: 10.1137/0804018 – ident: CR17 – year: 1987 ident: CR16 publication-title: Practical Methods of Optimization – volume: 22 start-page: 111 year: 2002 end-page: 131 ident: CR4 article-title: Parallel variable distribution for constrained optimization publication-title: Comput. Optim. Appli. doi: 10.1023/A:1014890403681 – volume: 8 start-page: 187 year: 1998 end-page: 196 ident: CR13 article-title: On the convergence of constrained parallel variable distribution algorithms publication-title: SIAM J. Optimization doi: 10.1137/S1052623495293949 – volume: 29 start-page: 11 year: 2003 end-page: 32 ident: CR10 article-title: A PVT-type algorithm for minimization a nonsmooth convex function publication-title: Serdica Math. J. – volume: 24 start-page: 269 year: 1992 end-page: 284 ident: CR1 article-title: A special newton-type optimization method publication-title: Optimization doi: 10.1080/02331939208843795 – volume: 4 start-page: 815 issue: 4 year: 1994 end-page: 832 ident: CR11 article-title: Parallel variable distribution publication-title: SIAM J. Optimization doi: 10.1137/0804047 – volume: 13 start-page: 1 year: 1999 ident: 300_CR7 publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008629511432 – volume: 8 start-page: 658 issue: 4 year: 1998 ident: 300_CR14 publication-title: SIAM J. Optimization doi: 10.1137/S1052623496309879 – volume-title: Parallel and Distributed Computation: Numerical Methods year: 1989 ident: 300_CR6 – volume: 4 start-page: 815 issue: 4 year: 1994 ident: 300_CR11 publication-title: SIAM J. Optimization doi: 10.1137/0804047 – volume: 24 start-page: 269 year: 1992 ident: 300_CR1 publication-title: Optimization doi: 10.1080/02331939208843795 – volume: 26 start-page: 346 year: 1988 ident: 300_CR18 publication-title: SIAM J. Control Optim. – volume: 211 start-page: 434 year: 2009 ident: 300_CR5 publication-title: Applied Mathematics and Computation doi: 10.1016/j.amc.2009.01.081 – volume-title: Numerical Analysis year: 1972 ident: 300_CR8 – volume: 4 start-page: 331 issue: 2 year: 1994 ident: 300_CR2 publication-title: SIAM J. Optimization doi: 10.1137/0804018 – volume: 7 start-page: 165 year: 1997 ident: 300_CR12 publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008618009738 – ident: 300_CR17 – volume: 17 start-page: 85 year: 2000 ident: 300_CR3 publication-title: Comput. Optim. Appl. doi: 10.1023/A:1008731209637 – ident: 300_CR15 – volume: 8 start-page: 187 year: 1998 ident: 300_CR13 publication-title: SIAM J. Optimization doi: 10.1137/S1052623495293949 – volume: 1 start-page: 70 year: 1993 ident: 300_CR9 publication-title: Mathematics in Economics – volume: 22 start-page: 111 year: 2002 ident: 300_CR4 publication-title: Comput. Optim. Appli. doi: 10.1023/A:1014890403681 – volume-title: Practical Methods of Optimization year: 1987 ident: 300_CR16 – volume: 29 start-page: 11 year: 2003 ident: 300_CR10 publication-title: Serdica Math. J. |
| SSID | ssj0017367 |
| Score | 2.0887897 |
| Snippet | In this paper, two PVD-type algorithms are proposed for solving inseparable linear constraint optimization. Instead of computing the residual gradient... |
| SourceID | crossref springer chongqing |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 707 |
| SubjectTerms | Applications of Mathematics Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical 全局收敛性 坐标旋转 并行算法 并行计算 最小化问题 梯度函数 线性约束优化 非线性规划 |
| Title | Parallel Algorithms for Large-scale Linearly Constrained Minimization Problem |
| URI | http://lib.cqvip.com/qk/85829X/201403/50241543.html https://link.springer.com/article/10.1007/s10255-013-0300-9 |
| Volume | 30 |
| WOSCitedRecordID | wos000341462800014&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1618-3932 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0017367 issn: 0168-9673 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/eLvHCXMwnV1LT8MwDI5gcIADb8TGQzlwAkXKmjZtjggxcdk0iYd2i9I8tkldB23h95P0BZMACe5u2tpO_FmOPwNwGUYm9pgQyFDmIccGgoRUErGYWA9gSlBqymET4WgUTSZsXPdx581t96YkWZ7UX5rdLPxF5TQCgjFi62AjcGQzLkV_eG5LByGhVY80tTuZhqQpZX63hCNUmC3T6at93WpgWq2KlsFmsPuvz9wDOzW2hDeVM-yDNZ0egO1hS8yaH4LhWGRuekoCRTJdZvNitsihxa0wcTfCUW4tpqFDno73GEoHHt0MCa2g4yBZ1E2bsB5DcwSeBnePt_eonqiAJOn7BWJeSFVgAiVDI4iyB6Fn0XVg-toLtDWLtGDFplAKGyoiFZHIJ6RkFPSxiZhnyDHopMtUnwDIjFbUZTdxjH1p_MjGecEMM30sYuOZLui1quUvFXMGD7ADDD7pAtzomsuai9z9TsI_WZSdGrlVI3dq5KwLrtpHmuV-Eb5ujMPrPZn_LN37k_Qp2LKgya-u7J6BTpG96XOwKd-LeZ5dlL74Aa-U15g |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFD7oFNQH7-LmLQ8-KYGuadPmUcQxcRsDp-wtpEmzDXbRdfr7TXrTgQr6nqbtOSc5Xzg53wdwGYQ6cpkQWFPmYssGgoVUErOImAhgSlCqU7GJoNMJ-33Wzfu4k-K2e1GSTHfqL81uBv7iVI2AOA5mq7DmWZUde0R_fC5LBwGhWY80NSuZBqQoZX43hSVUGM6mg1fzuuXEtFwVTZNNY-dfn7kL2zm2RDdZMOzBSjzdh612ScyaHEC7K-ZWPWWMxHgwm48Ww0mCDG5FY3sjHCfGYzGyyNPyHiNpwaPVkIgVshwkk7xpE-UyNIfw1Ljr3TZxrqiAJal7C8zcgCpf-0oGWhBlNkLXoGtf12PXj41bpAEr5gilHE1FqEISeoSkjIKeo0PmanIElelsGh8DYjpW1J5uosjxpPZCk-cF00zXHRFpV1ehVpqWv2TMGdx3LGDwSBWcwtZc5lzk9nfG_JNF2ZqRGzNya0bOqnBVPlJM98vg68I5PF-Tyc-ja38afQEbzV67xVv3nYcT2DQAysuu755CZTF_i89gXb4vRsn8PI3LD9PD2nw |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3JTsMwEB2xCcGBHVFWHziBrKZx4sRHBFQgoKrYxM1y7Lit1KalCXw_dpZCJUBC3Cd2MrYzz5qZ9wCOg1BHLhMCa8pcbNlAsJBKYhYRswOYEpTqXGwiaLXClxfWLnVO06ravUpJFj0NlqUpyeojpetfGt8MFMa5MgFxHMxmYd4zFxlb03X_8DxJIwSEFv3S1JxqGpAqrfndEJZcoTtMOq9m6ukgNZ0hzQNPc_Xfr7wGKyXmRGfFJlmHmTjZgOW7CWFrugl3bTG2qip9JPqd4biXdQcpMngW9W2lOE7NSsbIIlLLh4ykBZVWWyJWyHKTDMpmTlTK02zBU_Py8fwKl0oLWJKGl2HmBlT52lcy0IIo84N0Der2dSN2_dgslzQgxlytlKOpCFVIQo-QnGnQc3TIXE22YS4ZJvEOIKZjRe2tJ4ocT2ovNPFfMM10wxGRdnUNdidu5qOCUYP7jgUSHqmBU_mdy5Kj3H5On3-yK1s3cuNGbt3IWQ1OJo9Uw_1ifFotFC_Pavqz9e6frI9gsX3R5LfXrZs9WDK4yiuqevdhLhu_xQewIN-zXjo-zLfoB7cK42A |
| 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=Parallel+algorithms+for+large-scale+linearly+constrained+minimization+problem&rft.jtitle=Acta+Mathematicae+Applicatae+Sinica&rft.au=Han%2C+Cong-ying&rft.au=Zheng%2C+Fang-ying&rft.au=Guo%2C+Tian-de&rft.au=He%2C+Guo-ping&rft.date=2014-07-01&rft.issn=0168-9673&rft.eissn=1618-3932&rft.volume=30&rft.issue=3&rft.spage=707&rft.epage=720&rft_id=info:doi/10.1007%2Fs10255-013-0300-9&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10255_013_0300_9 |
| thumbnail_s | http://cvtisr.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fimage.cqvip.com%2Fvip1000%2Fqk%2F85829X%2F85829X.jpg |