Pointwise and global well-posedness in set optimization: a direct approach

被引：34

作者：

Crespi, Giovanni P. ^{[1
]}

Dhingra, Mansi ^{[2
]}

Lalitha, C. S. ^{[3
]}

机构：

[1] Univ Insubria, Dept Econ, Via Monte Generoso 71, I-21100 Varese, Italy

[2] Univ Delhi, Dept Math, Delhi 110007, India

[3] Univ Delhi, Dept Math, South Campus,Benito Jaurez Rd, New Delhi 110021, India

来源：

ANNALS OF OPERATIONS RESEARCH | 2018年 / 269卷 / 1-2期

关键词：

Well-posedness; Set optimization; l-minimal solution; Compactness; Upper continuity; SCALARIZATION;

D O I：

10.1007/s10479-017-2709-7

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：

The aim of this paper is to characterize some of the pointwise and global well-posedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The characterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness.

引用

页码：149 / 166

页数：18

共 20 条

[1]

[Anonymous], 1993, Lecture Notes in Mathematics

[2]

Bednarczuk E., 1987, Lecture notes in economics and mathematical systems, V294, P51

[3]

Crespi GP, 2007, J OPTIMIZ THEORY APP, V132, P213, DOI [10.1007/s10957-006-9144-2, 10.1007/S10957-006-9144-2]

[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] 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

[6] Well-setness and scalarization in set optimization [J].

Dhingra, Mansi ;

Lalitha, C. S. .

OPTIMIZATION LETTERS, 2016, 10 (08) :1657-1667

[7] Scalarization for pointwise well-posed vectorial problems [J].

Durea, M. .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2007, 66 (03) :409-418

[8]

Gopfert A., 2003, Variational Methods in Partially Ordered Spaces

[9] 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

[10] Nonconvex scalarization in set optimization with set-valued maps [J].

Hernandez, E. ;

Rodriguez-Marin, L. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) :1-18

← 1 2 →