Optimality of Mathematical Programming Problems with Rough Convexity of Objective Function
[1]
Ebrahim A. Youness, Department of Mathematics, Tanta University, Tanta, Egypt.
[2]
Ahmed A. Alsaraireh, Department of Computer Information Systems, The University of Jordan, Aqaba, Jordan.
The concept of convexity of sets and functions plays an important role in the field of mathematical programming. Convexity ensures the globality of solutions. In real life problems, the convexity might not be satisfied. So in this study, an optimality of a nonlinear programming problem in which the objective function is rough convex with respect to a family of convex functions is discussed. The sufficient and the necessary Kuhn Tucker conditions of optimality for these kind of problems is presented. An illustrative example are presented to clarify the results. Finally the results of this study will be used in many field such as: mathematical programming, engineering, and other sciences.
Rough Convexity, Rough Nonlinear Programming Problem, Kuhn Tucker Saddle Point, Kuhn Tucker Conditions
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