Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming

被引：3

作者：

Andreani, Roberto ^{[1
]}

Fukuda, Ellen H. ^{[2
]}

Haeser, Gabriel ^{[3
]}

Santos, Daiana O. ^{[4
]}

Secchin, Leonardo D. ^{[5
]}

机构：

[1] Univ Estadual Campinas, Dept Appl Math, Campinas, SP, Brazil

[2] Kyoto Univ, Grad Sch Informat, Kyoto, Japan

[3] Univ Sao Paulo, Dept Appl Math, Sao Paulo, SP, Brazil

[4] Univ Fed Sao Paulo, Paulista Sch Polit Econ & Business, Osasco, SP, Brazil

[5] Univ Fed Espirito Santo, Dept Appl Math, Sao Mateus, ES, Brazil

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2024年 / 200卷 / 01期

基金：

日本学术振兴会;

关键词：

Second-order cones; Symmetric cones; Optimality conditions; Constraint qualifications; Augmented Lagrangian method; OPTIMIZATION METHODS; GRADIENT DESCENT;

D O I：

10.1007/s10957-023-02338-6

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Nonlinear symmetric cone programming (NSCP) generalizes important optimization problems such as nonlinear programming, nonlinear semi-definite programming and nonlinear second-order cone programming (NSOCP). In this work, we present two new optimality conditions for NSCP without constraint qualifications, which implies the Karush-Kuhn-Tucker conditions under a condition weaker than Robinson's constraint qualification. In addition, we show the relationship of both optimality conditions in the context of NSOCP, where we also present an augmented Lagrangian method with global convergence to a KKT point under a condition weaker than Robinson's constraint qualification.

引用

页码：1 / 33

页数：33

共 50 条

[21] Statistical Inference of Second-Order Cone Programming
Zhang, Liwei
Gao, Shengzhe
Guo, Saoyan
ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, 2019, 36 (02)
[22] Statistical Inference of Second-Order Cone Programming
Wang, Jiani
Zhang, Liwei
ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, 2018, 35 (06)
[23] The Use of Squared Slack Variables in Nonlinear Second-Order Cone Programming
Fukuda, Ellen H.
Fukushima, Masao
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 170 (02) : 394 - 418
[24] On the existence of saddle points for nonlinear second-order cone programming problems
Jinchuan Zhou
Jein-Shan Chen
Journal of Global Optimization, 2015, 62 : 459 - 480
[25] On the existence of saddle points for nonlinear second-order cone programming problems
Zhou, Jinchuan
Chen, Jein-Shan
JOURNAL OF GLOBAL OPTIMIZATION, 2015, 62 (03) : 459 - 480
[26] The Use of Squared Slack Variables in Nonlinear Second-Order Cone Programming
Ellen H. Fukuda
Masao Fukushima
Journal of Optimization Theory and Applications, 2016, 170 : 394 - 418
[27] THE SECOND-ORDER OPTIMALITY CONDITIONS FOR VARIABLE PROGRAMMING
Yanping Wang Department of Economics
JournalofComputationalMathematics, 2008, 26 (05) : 756 - 766
[28] The second-order optimality conditions for variable programming
Wang, Yanping
Wang, Chuanlong
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2008, 26 (05) : 756 - 766
[29] Necessary and sufficient conditions for Farkas' lemma for cone systems and second-order cone programming duality
Jeyakumar, V.
Kum, S.
Lee, G. M.
JOURNAL OF CONVEX ANALYSIS, 2008, 15 (01) : 63 - 71
[30] SVM training: Second-order cone programming versus quadratic programming
Debnath, Rameswar
Takahashi, Haruhisa
2006 IEEE INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORK PROCEEDINGS, VOLS 1-10, 2006, : 1162 - +

← 1 2 3 4 5 →