Weak sharp minima for semi-infinite optimization problems with applications

被引：23
|
作者：
Zheng, Xi Yin [1 ]
Yang, Xiao Qi
机构：
[1] Yunnan Univ, Dept Math, Kunming 650091, Peoples R China
[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
来源：
SIAM JOURNAL ON OPTIMIZATION | 2007年 / 18卷 / 02期
关键词：
semi-infinite optimization; sharp minima; weak sharp minima; subdifferential; normal cone;
D O I：
10.1137/060670213
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study local weak sharp minima and sharp minima for smooth semi- infinite optimization problems SIP. We provide several dual and primal characterizations for a point to be a sharp minimum or a weak sharp minimum of SIP. As applications, we present several sufficient and necessary conditions of calmness for infinitely many smooth inequalities. In particular, we improve some calmness results in [ R. Henrion and J. Outrata, Math. Program., 104 ( 2005), pp. 437 - 464].
引用
收藏
页码：573 / 588
页数：16
相关论文
共 50 条
  • [31] A nonlinear norm-relaxed method for finely discretized semi-infinite optimization problems
    Xu, Qing-Juan
    Jian, Jin-Bao
    NONLINEAR DYNAMICS, 2013, 73 (1-2) : 85 - 92
  • [32] A transformation-based discretization method for solving general semi-infinite optimization problems
    Schwientek, Jan
    Seidel, Tobias
    Kuefer, Karl-Heinz
    MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2021, 93 (01) : 83 - 114
  • [33] Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems
    Nguyen Minh Tung
    Mai Van Duy
    4OR, 2023, 21 : 151 - 176
  • [34] Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems
    Nguyen Minh Tung
    Mai Van Duy
    4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH, 2023, 21 (01): : 151 - 176
  • [35] A nonlinear norm-relaxed method for finely discretized semi-infinite optimization problems
    Qing-Juan Xu
    Jin-Bao Jian
    Nonlinear Dynamics, 2013, 73 : 85 - 92
  • [36] WEAK SHARP MINIMA ON RIEMANNIAN MANIFOLDS
    Li, Chong
    Mordukhovich, Boris S.
    Wang, Jinhua
    Yao, Jen-Chih
    SIAM JOURNAL ON OPTIMIZATION, 2011, 21 (04) : 1523 - 1560
  • [37] Stability properties of weak sharp minima
    Studniarski, M
    Taha, AWA
    CONTROL AND CYBERNETICS, 2003, 32 (02): : 351 - 359
  • [38] New characterizations of weak sharp minima
    Jinchuan Zhou
    Changyu Wang
    Optimization Letters, 2012, 6 : 1773 - 1785
  • [39] New characterizations of weak sharp minima
    Zhou, Jinchuan
    Wang, Changyu
    OPTIMIZATION LETTERS, 2012, 6 (08) : 1773 - 1785
  • [40] On generic one-parametric semi-infinite optimization
    Jongen, HT
    Stein, O
    SIAM JOURNAL ON OPTIMIZATION, 1997, 7 (04) : 1103 - 1137
12345