The stability and extended well-posedness of the solution sets for set optimization problems via the Painleve-Kuratowski convergence

被引：23

作者：

Han, Yu ^{[1
]}

Zhang, Kai ^{[1
]}

Huang, Nan-jing ^{[2
]}

机构：

[1] Jiangxi Univ Finance & Econ, Sch Stat, Nanchang 330013, Jiangxi, Peoples R China

[2] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

来源：

MATHEMATICAL METHODS OF OPERATIONS RESEARCH | 2020年 / 91卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Set optimization problem; Painleve-Kuratowski convergence; Stability; Extended well-posedness; PAINLEV; -KURATOWSKI CONVERGENCES; POINTWISE;

D O I：

10.1007/s00186-019-00695-5

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：

In this paper, we obtain the Painleve-Kuratowski upper convergence and the Painleve-Kuratowski lower convergence of the approximate solution sets for set optimization problems with the continuity and convexity of objective mappings. Moreover, we discuss the extended well-posedness and the weak extended well-posedness for set optimization problems under some mild conditions. We also give some examples to illustrate our main results.

引用

页码：175 / 196

页数：22

共 33 条

[1] Set-relations and optimality conditions in set-valued maps [J].

Alonso, M ;

Rodríguez-Marín, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (08) :1167-1179

[2]

[Anonymous], 2004, VARIATIONAL ANAL

[3]

Aubin JP., 1984, Applied nonlinear analysis

[4] Extended Well-Posedness of Quasiconvex Vector Optimization Problems [J].

Crespi, G. P. ;

Papalia, M. ;

Rocca, M. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 141 (02) :285-297

[5] Pointwise and global well-posedness in set optimization: a direct approach [J].

Crespi, Giovanni P. ;

Dhingra, Mansi ;

Lalitha, C. S. .

ANNALS OF OPERATIONS RESEARCH, 2018, 269 (1-2) :149-166

[6] Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization [J].

Crespi, Giovanni P. ;

Kuroiwa, Daishi ;

Rocca, Matteo .

ANNALS OF OPERATIONS RESEARCH, 2017, 251 (1-2) :89-104

[7] CONVEXITY AND GLOBAL WELL-POSEDNESS IN SET-OPTIMIZATION [J].

Crespi, Giovanni P. ;

Kuroiwa, Daishi ;

Rocca, Matteo .

TAIWANESE JOURNAL OF MATHEMATICS, 2014, 18 (06) :1897-1908

[8] Painleve-Kuratowski Convergences of the Solution Sets to Perturbed Generalized Systems [J].

Fang, Zhi-miao ;

Li, Sheng-jie .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2012, 28 (02) :361-370

[9]

Gopfert A., 2003, Variational methods in partially ordered spaces

[10] Pointwise well-posedness in set optimization with cone proper sets [J].

Gutierrez, C. ;

Miglierina, E. ;

Molho, E. ;

Novo, V. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) :1822-1833

← 1 2 3 4 →