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

Abstract

In this paper, we explore the semi-infinite programming on smooth manifolds. We first discuss the optimality conditions for semi-infinite programming on smooth manifolds via homeomorphic optimality conditions for the associated problems. Further, we present Lagrange, Mond-Weir, and Wolfe type duality for the semi-infinite programming on manifolds, and examine weak and strong duality relations under the ϕ −1 -convexity assumption.