The minimizer of the sum of two strongly convex functions
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the functions is not available, limiting information to individual mini...
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| Veröffentlicht in: | Optimization Jg. 74; H. 16; S. 4357 - 4397 |
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| Sprache: | Englisch |
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Taylor & Francis
10.12.2025
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| ISSN: | 0233-1934, 1029-4945 |
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| Abstract | The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the functions is not available, limiting information to individual minimizers and convexity parameters - either due to privacy concerns or the nature of solution analysis - necessitates an exploration of the region encompassing potential minimizers based solely on these known quantities. The characterization of this region becomes notably intricate when dealing with multivariate strongly convex functions compared to the univariate case. This paper contributes outer and inner approximations for the region harboring the minimizer of the sum of two strongly convex functions, given a constraint on the norm of the gradient at the minimizer of the sum. Notably, we explicitly delineate the boundaries and interiors of both the outer and inner approximations. Intriguingly, the boundaries as well as the interiors turn out to be identical. Furthermore, we establish that the boundary of the region containing potential minimizers aligns with that of the outer and inner approximations. |
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| AbstractList | The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the functions is not available, limiting information to individual minimizers and convexity parameters – either due to privacy concerns or the nature of solution analysis – necessitates an exploration of the region encompassing potential minimizers based solely on these known quantities. The characterization of this region becomes notably intricate when dealing with multivariate strongly convex functions compared to the univariate case. This paper contributes outer and inner approximations for the region harboring the minimizer of the sum of two strongly convex functions, given a constraint on the norm of the gradient at the minimizer of the sum. Notably, we explicitly delineate the boundaries and interiors of both the outer and inner approximations. Intriguingly, the boundaries as well as the interiors turn out to be identical. Furthermore, we establish that the boundary of the region containing potential minimizers aligns with that of the outer and inner approximations. |
| Author | Sundaram, Shreyas Kuwaranancharoen, Kananart |
| Author_xml | – sequence: 1 givenname: Kananart surname: Kuwaranancharoen fullname: Kuwaranancharoen, Kananart email: kananart.kuwaranancharoen@intel.com, kkuwaran@purdue.edu organization: Intel Corporation – sequence: 2 givenname: Shreyas surname: Sundaram fullname: Sundaram, Shreyas organization: Purdue University |
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| References | e_1_3_3_52_1 e_1_3_3_75_1 Goebel R (e_1_3_3_63_1) 2008; 15 e_1_3_3_50_1 e_1_3_3_77_1 e_1_3_3_71_1 e_1_3_3_79_1 Nedić A. (e_1_3_3_17_1) 2018 e_1_3_3_18_1 e_1_3_3_39_1 e_1_3_3_14_1 e_1_3_3_37_1 e_1_3_3_90_1 e_1_3_3_16_1 e_1_3_3_35_1 e_1_3_3_58_1 e_1_3_3_10_1 e_1_3_3_33_1 e_1_3_3_56_1 e_1_3_3_12_1 e_1_3_3_31_1 e_1_3_3_54_1 e_1_3_3_73_1 e_1_3_3_40_1 e_1_3_3_86_1 e_1_3_3_61_1 e_1_3_3_88_1 e_1_3_3_7_1 e_1_3_3_9_1 e_1_3_3_29_1 e_1_3_3_25_1 e_1_3_3_48_1 e_1_3_3_27_1 e_1_3_3_46_1 e_1_3_3_69_1 e_1_3_3_80_1 e_1_3_3_3_1 e_1_3_3_21_1 e_1_3_3_44_1 e_1_3_3_67_1 e_1_3_3_82_1 e_1_3_3_5_1 e_1_3_3_23_1 e_1_3_3_42_1 e_1_3_3_65_1 e_1_3_3_84_1 e_1_3_3_30_1 e_1_3_3_51_1 e_1_3_3_76_1 e_1_3_3_78_1 e_1_3_3_70_1 Montgomery DC (e_1_3_3_43_1) 2021 e_1_3_3_19_1 e_1_3_3_13_1 e_1_3_3_38_1 e_1_3_3_59_1 e_1_3_3_91_1 e_1_3_3_15_1 e_1_3_3_36_1 e_1_3_3_57_1 e_1_3_3_34_1 e_1_3_3_55_1 e_1_3_3_72_1 e_1_3_3_11_1 e_1_3_3_32_1 e_1_3_3_53_1 e_1_3_3_74_1 e_1_3_3_41_1 e_1_3_3_62_1 e_1_3_3_87_1 e_1_3_3_60_1 e_1_3_3_89_1 e_1_3_3_6_1 e_1_3_3_8_1 e_1_3_3_28_1 e_1_3_3_24_1 e_1_3_3_49_1 e_1_3_3_26_1 e_1_3_3_47_1 e_1_3_3_68_1 e_1_3_3_81_1 e_1_3_3_2_1 e_1_3_3_20_1 e_1_3_3_45_1 Yan M. (e_1_3_3_64_1) 2014; 21 e_1_3_3_66_1 e_1_3_3_83_1 e_1_3_3_4_1 e_1_3_3_22_1 e_1_3_3_85_1 |
| References_xml | – ident: e_1_3_3_33_1 – ident: e_1_3_3_79_1 doi: 10.1109/72.80341 – ident: e_1_3_3_29_1 doi: 10.1109/tac.2020.3008139 – ident: e_1_3_3_41_1 – ident: e_1_3_3_81_1 doi: 10.1109/tsp.2007.913164 – ident: e_1_3_3_72_1 doi: 10.1137/070697835 – ident: e_1_3_3_70_1 doi: 10.1137/s003614450037906x – ident: e_1_3_3_44_1 doi: 10.4135/9781412983433 – ident: e_1_3_3_65_1 doi: 10.1007/978-3-7908-2604-3_16 – ident: e_1_3_3_14_1 doi: 10.1109/tac.2011.2167817 – ident: e_1_3_3_8_1 doi: 10.1109/mcs.2016.2558401 – volume: 15 start-page: 263 issue: 2 year: 2008 ident: e_1_3_3_63_1 article-title: Local strong convexity and local lipschitz continuity of the gradient of convex functions publication-title: J Convex Anal – ident: e_1_3_3_86_1 doi: 10.1017/s0004972700027441 – ident: e_1_3_3_27_1 doi: 10.23919/ACC50511.2021.9483067 – ident: e_1_3_3_53_1 doi: 10.1137/120863290 – ident: e_1_3_3_38_1 – ident: e_1_3_3_21_1 doi: 10.1145/2933057.2933105 – ident: e_1_3_3_88_1 doi: 10.4153/cjm-1980-020-7 – ident: e_1_3_3_57_1 doi: 10.1016/j.laa.2014.10.011 – ident: e_1_3_3_32_1 – ident: e_1_3_3_54_1 doi: 10.1007/s11590-016-1058-9 – ident: e_1_3_3_84_1 doi: 10.1007/978-3-319-46128-1_50 – ident: e_1_3_3_62_1 doi: 10.1016/0304-4068(82)90026-x – ident: e_1_3_3_40_1 – ident: e_1_3_3_80_1 doi: 10.1109/ACSSC.2006.356622 – ident: e_1_3_3_7_1 doi: 10.1109/tac.2012.2203215 – ident: e_1_3_3_25_1 doi: 10.1109/tsipn.2019.2928176 – ident: e_1_3_3_13_1 doi: 10.1109/tac.2008.2009515 – ident: e_1_3_3_51_1 – ident: e_1_3_3_46_1 doi: 10.1109/5254.708428 – ident: e_1_3_3_4_1 doi: 10.1109/jproc.2014.2306253 – ident: e_1_3_3_73_1 doi: 10.1145/2184319.2184343 – ident: e_1_3_3_71_1 – ident: e_1_3_3_30_1 doi: 10.1109/tsipn.2024.3379844 – ident: e_1_3_3_56_1 doi: 10.1145/1015330.1015435 – ident: e_1_3_3_20_1 doi: 10.1137/16m1084316 – ident: e_1_3_3_58_1 doi: 10.1561/2200000050 – ident: e_1_3_3_76_1 doi: 10.1109/tac.1971.1099831 – ident: e_1_3_3_2_1 doi: 10.1561/2200000018 – ident: e_1_3_3_16_1 doi: 10.1146/annurev-control-060117-105131 – ident: e_1_3_3_85_1 doi: 10.1016/0022-247x(88)90113-8 – ident: e_1_3_3_50_1 doi: 10.23919/ACC45564.2020.9147407 – ident: e_1_3_3_69_1 doi: 10.5555/2188385.2343697 – ident: e_1_3_3_90_1 doi: 10.1287/moor.2016.0817 – ident: e_1_3_3_87_1 doi: 10.1006/jmaa.2000.7310 – ident: e_1_3_3_11_1 – ident: e_1_3_3_28_1 doi: 10.23919/ACC45564.2020.9147396 – volume-title: Introduction to linear regression analysis year: 2021 ident: e_1_3_3_43_1 – ident: e_1_3_3_36_1 – ident: e_1_3_3_61_1 doi: 10.1007/bf02592948 – ident: e_1_3_3_5_1 doi: 10.1109/tsg.2017.2720471 – ident: e_1_3_3_77_1 doi: 10.1016/0005-1098(71)90059-8 – ident: e_1_3_3_22_1 doi: 10.1109/tac.2018.2836919 – ident: e_1_3_3_78_1 doi: 10.1080/00207178908953472 – ident: e_1_3_3_52_1 doi: 10.1007/s11590-014-0795-x – ident: e_1_3_3_59_1 doi: 10.1007/978-3-319-91578-4 – ident: e_1_3_3_34_1 doi: 10.1109/ALLERTON.2015.7447103 – ident: e_1_3_3_45_1 doi: 10.1002/9781118548387 – ident: e_1_3_3_68_1 doi: 10.1214/12-sts400 – ident: e_1_3_3_47_1 doi: 10.1007/978-0-387-77242-4 – ident: e_1_3_3_75_1 doi: 10.1137/1.9781611971484 – volume-title: Distributed optimization over networks year: 2018 ident: e_1_3_3_17_1 – ident: e_1_3_3_39_1 doi: 10.1007/978-3-030-58951-6_27 – ident: e_1_3_3_6_1 doi: 10.1109/PES.2011.6039082 – ident: e_1_3_3_26_1 doi: 10.1145/3382734.3405748 – ident: e_1_3_3_49_1 doi: 10.1109/CDC.2018.8619735 – ident: e_1_3_3_66_1 – ident: e_1_3_3_3_1 doi: 10.1561/2200000016 – ident: e_1_3_3_91_1 doi: 10.1007/bf01400115 – ident: e_1_3_3_18_1 doi: 10.1016/j.arcontrol.2019.05.006 – ident: e_1_3_3_74_1 doi: 10.1137/1.9781611971217 – ident: e_1_3_3_15_1 doi: 10.1109/tac.2014.2364096 – ident: e_1_3_3_35_1 doi: 10.1561/2200000083 – ident: e_1_3_3_12_1 – ident: e_1_3_3_89_1 doi: 10.1561/2200000058 – ident: e_1_3_3_24_1 doi: 10.1109/ACC.2016.7526806 – ident: e_1_3_3_23_1 – ident: e_1_3_3_83_1 doi: 10.1109/tsp.2012.2194290 – ident: e_1_3_3_82_1 doi: 10.1109/tsp.2009.2024278 – ident: e_1_3_3_9_1 doi: 10.1109/jproc.2018.2817461 – ident: e_1_3_3_19_1 doi: 10.1109/tac.2011.2161027 – ident: e_1_3_3_48_1 doi: 10.1016/j.isprsjprs.2010.11.001 – ident: e_1_3_3_60_1 doi: 10.1007/s10107-020-01510-4 – ident: e_1_3_3_10_1 doi: 10.1109/CDC.2012.6426691 – ident: e_1_3_3_55_1 doi: 10.1007/978-0-387-84858-7 – volume: 21 start-page: 965 issue: 4 year: 2014 ident: e_1_3_3_64_1 article-title: Extension of convex function publication-title: J Convex Anal – ident: e_1_3_3_42_1 doi: 10.1002/0471704091 – ident: e_1_3_3_67_1 – ident: e_1_3_3_37_1 doi: 10.1007/978-3-030-63076-8_2 – ident: e_1_3_3_31_1 doi: 10.1109/tsipn.2022.3188456 |
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| SubjectTerms | Approximation Boundaries Convex analysis Convexity decentralized optimization fault-tolerant systems Interiors Optimization quadratic functions strongly convex functions |
| Title | The minimizer of the sum of two strongly convex functions |
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