New Optimality Conditions for a Nondifferentiable Fractional Semipreinvex Programming Problem

Yi-Chou Chen and Wei-Shih Du

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/527183

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:527183

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