Scalarization and pointwise well-posedness for set optimization problems

被引：44

作者：

Long, Xian-Jun ^{[1
]}

Peng, Jian-Wen ^{[2
]}

Peng, Zai-Yun ^{[3
]}

机构：

[1] Chongqing Technol & Business Univ, Coll Math & Stat, Chongqing 400067, Peoples R China

[2] Chongqing Normal Univ, Sch Math, Chongqing 400047, Peoples R China

[3] Chongqing JiaoTong Univ, Coll Sci, Chongqing 400074, Peoples R China

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2015年 / 62卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Well-posedness; Set optimization problem; Nonlinear scalarization function; u-minimal solution; VECTOR OPTIMIZATION; VARIATIONAL PRINCIPLE; CONVEXITY;

D O I：

10.1007/s10898-014-0265-0

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 consider three kinds of pointwise well-posedness for set optimization problems. We establish some relations among the three kinds of pointwise well-posedness. By virtue of a generalized nonlinear scalarization function, we obtain the equivalence relations between the three kinds of pointwise well-posedness for set optimization problems and the well-posedness of three kinds of scalar optimization problems, respectively.

引用

页码：763 / 773

页数：11

共 30 条

[1]

[Anonymous], 1995, Mathematics and Its Applications

[2]

[Anonymous], 2007, Nonlinear Anal

[3]

[Anonymous], 2008, NONLINEAR ANAL

[4]

[Anonymous], 1966, COMP MATH MATH PHYS+, DOI DOI 10.1016/0041-5553(66)90003-6

[5]

[Anonymous], 2003, Variational Methods in Partially Ordered Spaces

[6]

[Anonymous], 1968, TOPOLOGY

[7]

[Anonymous], 1987, Lecture notes in economics and mathematical systems

[8]

[Anonymous], 1989, Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems

[9] Four types of nonlinear scalarizations and some applications in set optimization [J].

Araya, Yousuke .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (09) :3821-3835

[10]

Bednarczuk E., 1994, Control and Cybernetics, V23, P107

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