Optimality conditions in convex multiobjective SIP

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk–Kuhn–Tucker multipliers or a new gap function associated with the given problem.This research was partially cosponsored by the Ministry of Economy and Competitiveness (MINECO) of Spain, and by the European Regional Development Fund (ERDF) of the European Commission, Project MTM2014-59179-C2-1-P

Necessary optimality conditions for nonsmooth semi-infinite programming problems

Optimality condition, Semi-infinite programming, Nonsmooth analysis, Constraint qualification,

On Frèchet normal cone for nonsmooth mathematical programming problems with switching constraints

This paper is devoted to the study of a class of nonsmooth programming problems with switching constraints (abbreviated as, (NMPSC)), where all the involved functions in the switching constraints are assumed to be locally Lipschitz. We investigate the properties of Frèchet normal cone of (NMPSC). In particular, we introduce two Guignard type constraint qualifications for (NMPSC) in terms of Michel-Penot subdifferential. Moreover, we derive two estimates for the Fr‘echet normal cone of (NMPSC) and further establish stationarity conditions at an optimal solution for (NMPSC). To the best of our knowledge, this is for the first time Frèchet normal cone for (NMPSC) have been studied in the setting of Euclidean spaces