Continuity of cone-convex functions

被引：10

作者：

Kuwano, Issei ^{[1
]}

Tanaka, Tamaki ^{[1
]}

机构：

[1] Niigata Univ, Grad Sch Sci & Technol, Niigata 9502181, Japan

来源：

OPTIMIZATION LETTERS | 2012年 / 6卷 / 08期

基金：

日本学术振兴会;

关键词：

Set-valued maps; Nonconvex scalarization; Cone-convexity; Cone-continuity; Lipschitz continuity; SET CONTAINMENTS; OPTIMIZATION;

D O I：

10.1007/s11590-011-0381-4

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 the paper, we show continuity of cone-convex set-valued maps by using nonconvex scalarization methods for sets.

引用

页码：1847 / 1853

页数：7

共 15 条

[1] Well-positioned closed convex sets and well-positioned closed convex functions [J].

Adly, S ;

Ernst, E ;

Théra, M .

JOURNAL OF GLOBAL OPTIMIZATION, 2004, 29 (04) :337-351

[2] Dual characterizations of the set containments with strict cone-convex inequalities in Banach spaces [J].

Doagooei, A. R. ;

Mohebi, H. .

JOURNAL OF GLOBAL OPTIMIZATION, 2009, 43 (04) :577-591

[3]

Ekeland I., 1976, Convex Analysis and Variational Problems

[4]

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

[5]

Hamel A, 2006, J NONLINEAR CONVEX A, V7, P19

[6] 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

[7] Semi-Infinite Optimization under Convex Function Perturbations: Lipschitz Stability [J].

Huy, N. Q. ;

Yao, J. -C. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2011, 148 (02) :237-256

[8]

Jahn J., 2004, VECTOR OPTIMIZATION, P2011

[9] Characterizations of solution sets of convex vector minimization problems [J].

Jeyakumar, V. ;

Lee, G. M. ;

Dinh, N. .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2006, 174 (03) :1380-1395

[10] Characterizing set containments involving infinite convex constraints and reverse-convex constraints [J].

Jeyakumar, V .

SIAM JOURNAL ON OPTIMIZATION, 2003, 13 (04) :947-959

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