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