On approximate quasi Pareto solutions in nonsmooth semi-infinite interval-valued vector optimization problems

被引:10
作者
Nguyen Huy Hung [1 ]
Hoang Ngoc Tuan [1 ]
Nguyen Van Tuyen [1 ]
机构
[1] Hanoi Pedag Univ Phuc Yen, Dept Math, Vinh Phuc, Vietnam
关键词
KKT optimality conditions; duality relations; limiting; Mordukhovich subdifferential; approximate quasi Pareto solutions; nonsmooth semi-infinite interval-valued vector optimization; TUCKER OPTIMALITY CONDITIONS; MULTIOBJECTIVE PROGRAMMING-PROBLEMS; DUALITY; KKT;
D O I
10.1080/00036811.2022.2027385
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond-Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.
引用
收藏
页码:2432 / 2448
页数:17
相关论文
共 41 条
[1]  
Ahmad I., 2015, Control Cybern, V44, P19
[2]  
Alefeld G., 1983, INTRO INTERVAL COMPU, Vfirst edition
[3]  
[Anonymous], 2006, VARIATIONAL ANAL GEN
[4]  
Bao TQ, 2017, J CONVEX ANAL, V24, P393
[5]   Robust convex optimization [J].
Ben-Tal, A ;
Nemirovski, A .
MATHEMATICS OF OPERATIONS RESEARCH, 1998, 23 (04) :769-805
[6]   Selected topics in robust convex optimization [J].
Ben-Tal, Aharon ;
Nemirovski, Arkadi .
MATHEMATICAL PROGRAMMING, 2008, 112 (01) :125-158
[7]  
BenTal A, 2009, PRINC SER APPL MATH, P1
[8]   Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative [J].
Chalco-Cano, Y. ;
Lodwick, W. A. ;
Rufian-Lizana, A. .
FUZZY OPTIMIZATION AND DECISION MAKING, 2013, 12 (03) :305-322
[9]   Characterizations of solution sets for parametric multiobjective optimization problems [J].
Chen, Zhe .
APPLICABLE ANALYSIS, 2013, 92 (12) :2469-2479
[10]   Approximate solutions of multiobjective optimization problems [J].
Chuong, Thai Doan ;
Kim, Do Sang .
POSITIVITY, 2016, 20 (01) :187-207