Counterexample and Optimality Conditions in Differentiable Multiobjective Programming

被引：0

作者：

D. S. Kim

G. M. Lee

B. S. Lee

S. J. Cho

机构：

来源：

Journal of Optimization Theory and Applications | 2001年 / 109卷

关键词：

multiobjective programming; Pareto-optimal solutions; weak Pareto-optimal solutions; optimality conditions;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Recently, sufficient optimality theorems for (weak) Pareto-optimal solutions of a multiobjective optimization problem (MOP) were stated in Theorems 3.1 and 3.3 of Ref. 1. In this note, we give a counterexample showing that the theorems of Ref. 1 are not true. Then, by modifying the assumptions of these theorems, we establish two new sufficient optimality theorems for (weak) Pareto-optimal solutions of (MOP); moreover, we give generalized sufficient optimality theorems for (MOP).

引用

页码：187 / 192

页数：5

共 50 条

[1] Counterexample and optimality conditions in differentiable multiobjective programming
Kim, DS
Lee, GM
Lee, BS
Cho, SJ
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2001, 109 (01) : 187 - 192
[2] Optimality Conditions in Differentiable Multiobjective Programming
A. A. K. Majumdar
[J]. Journal of Optimization Theory and Applications, 1997, 92 : 419 - 427
[3] OPTIMALITY CONDITIONS IN MULTIOBJECTIVE DIFFERENTIABLE PROGRAMMING
SINGH, C
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1987, 53 (01) : 115 - 123
[4] Optimality conditions in differentiable multiobjective programming
Majumdar, AAK
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1997, 92 (02) : 419 - 427
[5] ON SOME SUFFICIENT OPTIMALITY CONDITIONS IN MULTIOBJECTIVE DIFFERENTIABLE PROGRAMMING
PREDA, V
[J]. KYBERNETIKA, 1992, 28 (04) : 263 - 270
[6] OPTIMALITY CONDITIONS FOR DIRECTIONALLY DIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING-PROBLEMS
ISHIZUKA, Y
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1992, 72 (01) : 91 - 111
[7] KKT optimality conditions in interval valued multiobjective programming with generalized differentiable functions
Singh, D.
Dar, B. A.
Kim, D. S.
[J]. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 2016, 254 (01) : 29 - 39
[8] OPTIMALITY CONDITIONS IN NONSMOOTH MULTIOBJECTIVE PROGRAMMING
WANG Liancheng
DONG Jiali
LIU Qinghuai (Depertment of Mathematics
[J]. Journal of Systems Science & Complexity, 1994, (03) : 250 - 255
[9] A NOTE ON OPTIMALITY CONDITIONS IN MULTIOBJECTIVE PROGRAMMING
汪寿阳
[J]. Journal of Systems Science & Complexity, 1988, (02) : 184 - 190
[10] Optimality Conditions for Nonsmooth Multiobjective Programming
Wang, Cailing
Zhang, You
Sun, Wenjuan
[J]. 2008 CHINESE CONTROL AND DECISION CONFERENCE, VOLS 1-11, 2008, : 3049 - +

← 1 2 3 4 5 →