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

Abstract

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.

Keywords:

• KKT optimality conditions
• duality relations
• limiting/Mordukhovich subdifferential
• approximate quasi Pareto solutions
• nonsmooth semi-infinite interval-valued vector optimization

AMS Classifications:

• 90C29
• 90C46
• 90C70
• 90C34
• 49J52

Acknowledgments

We would like to thank the anonymous referee for insightful comments and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is funded by the Hanoi Pedagogical University 2 [grant number HPU2.UT-2021.15].