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

被引：4

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; MULTIOBJECTIVE OPTIMIZATION; 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

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