New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

Abstract

We study a nondifferentiable fractional programming problem as follows: (P)minx∈Kf(x)/g(x) subject to x∈K⊆X, hi(x)≤0, i=1,2,…,m, where K is a semiconnected subset in a locally convex topological vector space X, f:K→ℝ, g:K→ℝ+ and hi:K→ℝ, i=1,2,…, m. If f, -g, and hi, i=1,2,…,m, are arc-directionally differentiable, semipreinvex maps with respect to a continuous map γ:[0,1]→K⊆X satisfying γ(0)=0 and γ′(0+)∈K, then the necessary and sufficient conditions for optimality of (P) are established.