On optimization problems with set-valued objective maps

被引：7
|
作者：
Maeda, Takashi [1 ]
机构：
[1] Kanazawa Univ, Fac Econ, Kanazawa, Ishikawa 9201192, Japan
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 03期
关键词：
Quasi ordering; Set-valued map; Convexity; Non-dominated solution; Weak non-dominated solution; Semi-weak non-dominated solution; Pareto optimal solution; OPTIMALITY CONDITIONS;
D O I：
10.1016/j.amc.2010.04.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider constrained optimization problems with set-valued objective maps. First, we define three types of quasi orderings on the set of all non-empty subsets in n-dimensional Euclidean space and investigate their properties. Next, by using these orderings, we define the concepts of the convexities to set-valued maps and investigate their properties. Finally, based on these results, we define the concepts of optimal solutions to constrained optimization problems with set-valued objective maps and characterize their properties. (C) 2010 Elsevier Inc. All rights reserved.
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页码：1150 / 1157
页数：8
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