Approximate weak efficiency of the set-valued optimization problem with variable ordering structures

被引:0
|
作者
Zhou, Zhiang [1 ]
Wei, Wenbin [2 ]
Huang, Fei [1 ]
Zhao, Kequan [2 ]
机构
[1] Chongqing Univ Technol, Coll Sci, Chongqing 400054, Peoples R China
[2] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
基金
国家重点研发计划;
关键词
Set-valued maps; Variable ordering structures; Approximate weakly efficient solution; Scalarization; BENSON PROPER EFFICIENCY; VECTOR OPTIMIZATION; NONDOMINATED SOLUTIONS; SEPARATION THEOREMS; OPTIMAL ELEMENTS; SCALARIZATION; RESPECT; POINTS; DUALITY;
D O I
10.1007/s10878-024-01211-0
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In locally convex spaces, we introduce the new notion of approximate weakly efficient solution of the set-valued optimization problem with variable ordering structures (in short, SVOPVOS) and compare it with other kinds of solutions. Under the assumption of near D(<middle dot>)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {D}(\cdot )$$\end{document}-subconvexlikeness, we establish linear scalarization theorems of (SVOPVOS) in the sense of approximate weak efficiency. Finally, without any convexity, we obtain a nonlinear scalarization theorem of (SVOPVOS). We also present some examples to illustrate our results.
引用
收藏
页数:13
相关论文
共 50 条
  • [1] SCALARIZATIONS OF BENSON NONDOMINATED SOLUTIONS OF SET-VALUED OPTIMIZATION PROBLEMS WITH VARIABLE ORDERING STRUCTURES IN LINEAR SPACES
    Zhou, Zhiang
    Wei, Wenbin
    Zhao, Kequan
    Liu, Caiping
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2023, 24 (02) : 435 - 446
  • [2] APPROXIMATE EFFICIENCY IN SET-VALUED OPTIMIZATION WITH VARIABLE ORDER
    Durea, Marius
    Florea, Elena-Andreea
    Maxim, Diana-Elena
    Strugariu, Radu
    JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2022, 6 (06): : 619 - 640
  • [3] Approximate Weak Minimal Solutions of Set-Valued Optimization Problems
    Khoshkhabar-amiranloo, S.
    JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA, 2023, 11 (03) : 673 - 692
  • [4] STRICT EFFICIENCY IN SET-VALUED OPTIMIZATION
    Flores-Bazan, Fabian
    Jimenez, Bienvenido
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) : 881 - 908
  • [5] Approximate quasi efficiency of set-valued optimization problems via weak subdifferential
    Das K.
    Nahak C.
    SeMA Journal, 2017, 74 (4) : 523 - 542
  • [6] OPTIMALITY CONDITIONS FOR APPROXIMATE SOLUTIONS OF SET-VALUED OPTIMIZATION PROBLEMS IN REAL LINEAR SPACES
    Kiyani, E.
    Vaezpour, S. M.
    Tavakoli, C. J.
    TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, 2021, 11 (02): : 395 - 407
  • [7] Approximate solutions and scalarization in set-valued optimization
    Dhingra, Mansi
    Lalitha, C. S.
    OPTIMIZATION, 2017, 66 (11) : 1793 - 1805
  • [8] Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces
    Liang, Hongwei
    Wan, Zhongping
    OPEN MATHEMATICS, 2019, 17 : 1168 - 1182
  • [9] Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem
    Chinaie, M.
    Fakhar, F.
    Fakhar, M.
    Hajisharifi, H. R.
    JOURNAL OF GLOBAL OPTIMIZATION, 2019, 75 (01) : 131 - 141
  • [10] VARIABLE ORDERING STRUCTURES IN SET OPTIMIZATION
    Koebis, Elisabeth
    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2017, 18 (09) : 1571 - 1589