Necessary conditions for weak minima and for strict minima of order two in nonsmooth constrained multiobjective optimization

Abstract

In this paper, we give necessary conditions for the existence of a strict local minimum of order two for multiobjective optimization problems with equality and inequality constraints. We suppose that the objective function and the active inequality constraints are only locally Lipschitz. We consider both regular equality constraints and degenerate equality constraints. This article could be considered as a continuation of [E. Constantin, Necessary Conditions for Weak Efficiency for Nonsmooth Degenerate Multiobjective Optimization Problems, J. Global Optim, 75, 111-129, 2019]. We introduce a constraint qualification and a regularity condition, and we show that under each of them, the dual necessary conditions for a weak local minimum of the aforementioned article become of Kuhn-Tucker type.