Abstract
We consider nondifferentiable minimax fractional programming problems involving B-(p, r)-invex functions with respect to η and b. Sufficient optimality conditions and duality results for a class of nondifferentiable minimax fractional programming problems are obtained undr B-(p, r)-invexity assumption on objective and constraint functions. Parametric duality, Mond-Weir duality, and Wolfe duality problems may be formulated, and duality results are derived under B-(p, r)-invex functions.
Highlights
Convexity plays an important role in many aspects of mathematical programming including sufficient optimality conditions and duality theorems
Strong, and strict converse duality theorems under the framework of B- p, r -invex with respect to the same function η and with respect to, not necessarily, the same function b
We use the optimality conditions of the preceding section and show that the following formation is a dual D to the minimax problem P : max sup k, s,t,y ∈K z z,μ,k,w,v ∈H1 s,t,y where H1 s, t, y denotes the set of z, μ, k, w, v ∈ Rn × Rp × R × Rn × Rn satisfying s p ti ∇f z, yi Bw − k ∇h z, yi − Dv ∇ μj gj z 0, 4.1
Summary
Convexity plays an important role in many aspects of mathematical programming including sufficient optimality conditions and duality theorems. In 11 , Lai and Lee employed the optimality conditions to construct two parameter-free dual models of nondifferentiable minimax fractional programming problem which involve pseudoconvex and quasiconvex functions, and derived weak and strong duality theorems. Strong, and strict converse duality theorems under the framework of B- p, r -invex with respect to the same function η and with respect to, not necessarily, the same function b
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