Optimality And Duality For Symmetrically Differentiable Multi-Objective Programming Involving Generalized B-(p,r)-invex Function

Multi-objective programming has been applied to a lot of fields. Studying onoptimality and duality has been one of the most important issues in the theory ofoptimization. In this thesis, multi-objective programming with inequality constraints areconcerned. First, on base of B (p,r) invex functions and SymmetricallyDifferentiable generalized Convex, new classes of functions called B and strict s (p,r) invexfunctionB_s (p,r) invex fuction are defined for multi-objectiveprogramming by using Minch’s symmetric gradient. The optimality for multi-objectiveprogramming is studied under the assumption of the new generalized convexity. Severalsufficient optimality conditions are obtained. The weak duality theorems, strong dualitytheorems and strict converse duality theorems are provered for Wolfe type andMond-Weir type dual problem. The saddle point optimality conditions for multi-objectivefractional programming problem are established by using the B, the s (p,r) invex function.SecondB_s (p,r) invex function is generalized. The new generalized uniformB_s (p,r) invex function and stictlty generalized uniform B_s (p,r) invex functionare introduced. By utilizing the new concepts, K-T necessary conditions and sufficientoptimality conditions are studied for multi-objective programming involving above newgeneralized uniform B_s (p,r) invex function. And Mond-Weir type dual areestablished. The weak duality, strong duality and strict converse duality theorems aregiven involving the generalized convexity. The saddle point optimality standard of amulti-objective fractional programming problem are established by using a newgeneralized uniform B_s (p,r) invex function.