New second-order necessary optimality conditions for constrained vector optimization problems

Abstract

This paper is devoted to second-order optimality conditions of constrained vector optimization problems with continuously Fréchet differentiable data. Different from conventional approaches, we employ a new one, image space analysis, to establish suitable regularity conditions and then present new second-order necessary optimality conditions that depend on one single KKT multiplier for all critical directions. Moreover, we propose one more regularity condition for the multiobjective case and compare it with the previous one. Besides, we compare the main regularity conditions with the existing ones in the literature for the scalar case.

Keywords:

• Second-order necessary optimality conditions
• constrained vector optimization problems
• image space analysis
• KKT multipliers
• regularity conditions

Mathematics Subject Classifications 2010::

• 90C46
• 90C29
• 49K99

Disclosure statement

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

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 11971078, 11571055 and 12201085] and the Science and Technology Research Program of Chongqing Municipal Education Commission [grant number KJQN202000740].