Abstract
In this paper, we concentrate our study to derive appropriate duality theorems for two types of second-order dual models of a nondifferentiable minimax fractional programming problem involving second-order α-univex functions. Examples to show the existence of α-univex functions have also been illustrated. Several known results including many recent works are obtained as special cases.
Highlights
1 Introduction After Schmitendorf [ ], who derived necessary and sufficient optimality conditions for static minimax problems, much attention has been paid to optimality conditions and duality theorems for minimax fractional programming problems [ – ]
Where Y is a compact subset of Rl, f (·, ·) : Rn × Rl → R, h(·, ·) : Rn × Rl → R are twice continuously differentiable on Rn × Rl and g(·) : Rn → Rm is twice continuously differentiable on Rn, B, and D are a n × n positive semidefinite matrix, f (x, y) + / ≥, and h(x, y) – / > for each (x, y) ∈ J × Y, where J = {x ∈ Rn : g(x) ≤ }
In addition, the assumptions of weak duality hold for all feasible solutions (x, μ, w, v, s, t, y, p) of (DM ), (x*, μ*, w*, v*, s*, t*, y*, p* = ) is an optimal solution of (DM )
Summary
After Schmitendorf [ ], who derived necessary and sufficient optimality conditions for static minimax problems, much attention has been paid to optimality conditions and duality theorems for minimax fractional programming problems [ – ]. We consider the following nondifferentiable minimax fractional programming problem: f (x, y) + (xT Bx) / Motivated by [ , , ], Yang and Hou [ ] formulated a dual model for fractional minimax programming problem and proved duality theorems under generalized convex functions.
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