tailieunhanh - Báo cáo hóa học: " Duality in nondifferentiable minimax fractional programming with B-(p, r)-invexity"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Duality in nondifferentiable minimax fractional programming with B-(p, r)-invexity | Ahmad et al. Journal of Inequalities and Applications 2011 2011 75 http content 2011 1 75 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Duality in nondifferentiable minimax fractional programming with B- p r -invexity Izhar Ahmad1 2 SK Gupta3 N Kailey4 and Ravi P Agarwal1 5 1 Correspondence drizhar@kfupm. department of Mathematics and Statistics King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia Full list of author information is available at the end of the article Springer Abstract In this article we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution to the problem and then establish weak strong and strict converse duality theorems for the problem and its dual problem under B- p r -invexity assumptions. Examples are given to show that B- p r -invex functions are generalization of p r -invex and convex functions AMS Subject Classification 90C32 90C46 49J35. Keywords nondifferentiable fractional programming optimality conditions B- p r -invex function duality theorems 1 Introduction The mathematical programming problem in which the objective function is a ratio of two numerical functions is called a fractional programming problem. Fractional programming is used in various fields of study. Most extensively it is used in business and economic situations mainly in the situations of deficit of financial resources. Fractional programming problems have arisen in multiobjective programming 1 2 game theory 3 and goal programming 4 . Problems of these type have been the subject of immense interest in the past few years. The necessary and sufficient conditions for generalized minimax programming were first developed by Schmitendorf 5 . Tanimoto 6 applied these optimality conditions to define a dual problem and derived duality theorems. Bector and Bhatia 7 relaxed the convexity .