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

被引：0
|
作者：
Roberto Andreani
Ellen H. Fukuda
Gabriel Haeser
Daiana O. Santos
Leonardo D. Secchin
机构：
[1] University of Campinas,Department of Applied Mathematics
[2] Kyoto University,Graduate School of Informatics
[3] University of São Paulo,Department of Applied Mathematics
[4] Federal University of São Paulo,Paulista School of Politics, Economics and Business
[5] Federal University of Espírito Santo,Department of Applied Mathematics
来源：
Journal of Optimization Theory and Applications | 2024年 / 200卷
关键词：
Second-order cones; Symmetric cones; Optimality conditions; Constraint qualifications; Augmented Lagrangian method;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：1 / 33
页数：32
相关论文
共 50 条
  • [1] Optimality Conditions for Nonlinear Second-Order Cone Programming and Symmetric Cone Programming
    Andreani, Roberto
    Fukuda, Ellen H.
    Haeser, Gabriel
    Santos, Daiana O.
    Secchin, Leonardo D.
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2024, 200 (01) : 1 - 33
  • [2] On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
    Fukuda, Ellen H.
    Haeser, Gabriel
    Mito, Leonardo M.
    [J]. SET-VALUED AND VARIATIONAL ANALYSIS, 2023, 31 (02)
  • [3] On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
    Ellen H. Fukuda
    Gabriel Haeser
    Leonardo M. Mito
    [J]. Set-Valued and Variational Analysis, 2023, 31
  • [4] On second-order optimality conditions for nonlinear programming
    Andreani, R.
    Martinez, J. M.
    Schuverdt, M. L.
    [J]. OPTIMIZATION, 2007, 56 (5-6) : 529 - 542
  • [5] Second-order cone programming
    F. Alizadeh
    D. Goldfarb
    [J]. Mathematical Programming, 2003, 95 : 3 - 51
  • [6] Second-order cone programming
    Alizadeh, F
    Goldfarb, D
    [J]. MATHEMATICAL PROGRAMMING, 2003, 95 (01) : 3 - 51
  • [7] A homotopy method for nonlinear second-order cone programming
    Li Yang
    Bo Yu
    YanXi Li
    [J]. Numerical Algorithms, 2015, 68 : 355 - 365
  • [8] A homotopy method for nonlinear second-order cone programming
    Yang, Li
    Yu, Bo
    Li, YanXi
    [J]. NUMERICAL ALGORITHMS, 2015, 68 (02) : 355 - 365
  • [9] No Gap Second-order Optimality Conditions for a Matrix Cone Programming Induced by the Nuclear Norm
    Zhang, Ning
    Zhang, Liwei
    [J]. ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, 2016, 33 (02)
  • [10] Applications of second-order cone programming
    Lobo, MS
    Vandenberghe, L
    Boyd, S
    Lebret, H
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 284 (1-3) : 193 - 228
12345