Non-differentiable minimax fractional programming with generalized -univexity

✍ Scribed by Anurag Jayswal

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 197 KB
• Volume: 214
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.02.007

✦ Synopsis

In this paper, we study a non-differentiable minimax fractional programming problem under the assumption of generalized -univex function. In this paper we extend the concept of -invexity [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequalities Pure Appl. Math. 5 (2004) 1-9] and pseudo -invexity [S.K. Mishra, M.A. Noor, On vector variational-like inequality problems, J. Math. Anal. Appl. 311 (2005) 69-75] to -univexity and pseudo -univexity from a view point of generalized convexity. We also introduce the concept of strict pseudo -univex and quasi -univex functions. We derive Karush-Kuhn-Tuckertype 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.