Non-differentiable minimax fractional programming with generalized alpha-univexity

摘要

In this paper, we study a non-differentiable minimax fractional programming problem under the assumption of generalized alpha-univex function. In this paper we extend the concept of alpha-invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo alpha-invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75] to alpha-univexity and pseudo a-univexity from a view point of generalized convexity. We also introduce the concept of strict pseudo alpha-univex and quasi a-univex 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 form of dual problems. The results in this paper extend a few known results in the literature. (C) 2007 Elsevier B.V. All rights reserved.