Generalized α-invexity and nondifferentiable minimax fractional programming

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In this paper, we study a nondifferentiable minimax fractional programming problem under the assumptions of α-invex function. In this paper we utilize the concept of α-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1–9] and pseudo-α-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69–75]. We also introduce the concept of strict pseudo-α-invex and quasi-α-invex functions. We derive Karush–Kuhn–Tucker-type sufficient optimality conditions and establish weak, strong and converse duality theorems for the problem and its three different dual problems. The results in this paper extend several known results in the literature.

论文关键词:26A51,49J35,90C32,Nondifferentiable minimax fractional programming problems,Duality,Sufficient optimality conditions,Generalized convexity,α-invexity

论文评审过程:Received 25 April 2006, Revised 6 June 2006, Available online 28 July 2006.

论文官网地址:https://doi.org/10.1016/j.cam.2006.06.009