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,h i(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. © 2013 yi-chou chen and wei-shih du.