New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

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

A class of r-semipreinvex functions and optimality in nonlinear programming

Semi-connected sets, Semipreinvex functions, r-Semipreinvex functions, Optimality, Nonlinear programming, 90C25, 90C26, 90C30,