Optimality conditions in convex multiobjective SIP

Abstract

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.

Recent contributions to linear semi-infinite optimization: an update

“…A data quali…cation involving c which is weaker than LFMCQ has been used in [155]. The above optimality theorem under CQs has been extended to in…nite optimization in di¤erent ways ( [57], [63], [75], [76], [153]), to multi-objective LSIO in [91,Theorem 23] and to multi-objective convex semi-in…nite optimization in [92] and [113].…”

Recent contributions to linear semi-infinite optimization

“…A data quali…cation involving c which is weaker than LFMCQ has been used in [135]. The above optimality theorem under CQs has been extended to in…nite optimization in di¤erent ways ( [48], [54], [65], [66], [133]), to multi-objective LSIO in [78,Theorem 23] and to multi-objective convex semi-in…nite optimization in [79] and [98].…”

Homeomorphic optimality conditions and duality for semi-infinite programming on smooth manifolds

“…The semi-infinite programming problems in Euclidean spaces are optimization problems with the infinite number of constraints. Due to their important meanings in theoretical aspect and practical applications, these problems have been recently studied in many papers, see e.g., [1,2,3,4,5,6,7,8,9,10,11] and the references therein.…”