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.
引用
收藏
页码：1150 / 1157
页数：8
相关论文
共 50 条
  • [41] METRIC ENTROPY FOR SET-VALUED MAPS
    Vivas, Kendry J.
    Sirvent, Victor F.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2022, 27 (11): : 6589 - 6604
  • [42] On various entropies of set-valued maps
    Wang, Xinsheng
    Zhang, Yu
    Zhu, Yujun
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 524 (02)
  • [43] Random Lifting of Set-Valued Maps
    Capuani, Rossana
    Marigonda, Antonio
    Mogentale, Marta
    LARGE-SCALE SCIENTIFIC COMPUTING (LSSC 2021), 2022, 13127 : 297 - 305
  • [44] TOPOLOGICAL ENTROPY FOR SET-VALUED MAPS
    Carrasco-Olivera, Dante
    Metzger Alvan, Roger
    Morales Rojas, Carlos Arnoldo
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (10): : 3461 - 3474
  • [45] ε-Subdifferentials of set-valued maps and ε-weak Pareto optimality for multiobjective optimization
    Taa, A
    MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2005, 62 (02) : 187 - 209
  • [46] ɛ-Subdifferentials of Set-valued Maps and ɛ-Weak Pareto Optimality for Multiobjective Optimization
    A. Taa
    Mathematical Methods of Operations Research, 2005, 62 : 187 - 209
  • [47] Super efficiency in vector optimization with nearly convexlike set-valued maps
    Mehra, A
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 276 (02) : 815 - 832
  • [48] ε-strict subdifferentials of set-valued maps and optimality conditions
    Zhou, Zhi-Ang
    Yang, Xin-Min
    Peng, Jian-Wen
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (09) : 3761 - 3775
  • [49] Generalized radial epiderivatives and nonconvex set-valued optimization problems
    Long, Xian-Jun
    Peng, Jian-Wen
    Wong, Mu-Ming
    APPLICABLE ANALYSIS, 2012, 91 (10) : 1891 - 1900
  • [50] Lagrange multipliers for set-valued optimization problems associated with coderivatives
    Ha, TXD
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 311 (02) : 647 - 663
12345