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

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...

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Bibliographic Details
Published in:Applicable analysis 2023-06, Vol.102 (9), p.2432-2448
Main Authors: Huy Hung, Nguyen, Ngoc Tuan, Hoang, Van Tuyen, Nguyen
Format: Article
Language:English
Subjects:
approximate quasi Pareto solutions
duality relations
KKT optimality conditions
limiting/Mordukhovich subdifferential
nonsmooth semi-infinite interval-valued vector optimization
Optimization
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Summary: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.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2022.2027385