Characterizations of efficient and weakly efficient points in nonconvex vector optimization

被引：3

作者：

Zhao, Ke Quan ^{[1
]}

Yang, Xin Min ^{[1
]}

机构：

[1] Chongqing Normal Univ, Coll Math Sci, Chongqing 401331, Peoples R China

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2015年 / 61卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Nonconvex vector optimization; Efficiency; Weak efficiency; Pseudoconvexity; Quasiconvexity; Linearizing cone; KUHN-TUCKER CONDITIONS; MULTIOBJECTIVE OPTIMIZATION; CONSTRAINT QUALIFICATIONS; OPTIMALITY CONDITIONS; PROPER EFFICIENCY; SOLUTION SETS; CONES; CONVEXITY; RESPECT;

D O I：

10.1007/s10898-014-0191-1

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, a class of nonconvex vector optimization problems with inequality constraints and a closed convex set constraint are considered. By means of Clarke derivatives and Clarke subdifferentials, a necessary and sufficient condition of weak efficiency and a sufficient criteria of efficiency are presented under suitable generalized convexity. A special case is discussed in finite dimensional space and an equivalent version of sufficient criteria of efficiency is obtained by means of Clarke derivative and linearizing cone. Some examples also are given to illustrate the main results.

引用

页码：575 / 590

页数：16

共 50 条

[1] Characterizations of efficient and weakly efficient points in nonconvex vector optimization
Ke Quan Zhao
Xin Min Yang
Journal of Global Optimization, 2015, 61 : 575 - 590
[2] A CHARACTERIZATION OF EFFICIENT AND WEAKLY EFFICIENT POINTS IN CONVEX VECTOR OPTIMIZATION
Winkler, Kristin
SIAM JOURNAL ON OPTIMIZATION, 2008, 19 (02) : 756 - 765
[3] Characterizations of efficient points in convex vector optimization problems
Winkler, K
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2001, 53 (02) : 205 - 214
[4] Characterizations of efficient points in convex vector optimization problems
Kristin Winkler
Mathematical Methods of Operations Research, 2001, 53 : 205 - 214
[5] Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization
Fernando García-Castaño
Miguel Ángel Melguizo-Padial
G. Parzanese
Mathematical Methods of Operations Research, 2023, 97 : 367 - 382
[6] Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization
Garcia-Castano, Fernando
Melguizo-Padial, Miguel Angel
Parzanese, G.
MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2023, 97 (03) : 367 - 382
[7] CHARACTERIZATIONS OF EFFICIENT SETS IN VECTOR OPTIMIZATION
BOISSARD, N
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1995, 51 (01) : 43 - 54
[8] Efficient and weakly efficient solutions for the vector topical optimization
Yao, C. L.
Li, S. J.
OPTIMIZATION LETTERS, 2018, 12 (08) : 1929 - 1945
[9] Efficient and weakly efficient solutions for the vector topical optimization
C. L. Yao
S. J. Li
Optimization Letters, 2018, 12 : 1929 - 1945
[10] Characterizations of nonemptiness and compactness of the set of weakly efficient solutions for convex vector optimization and applications
Huang, XX
Yang, XQ
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 264 (02) : 270 - 287

← 1 2 3 4 5 →