Mixed symmetric duality in multiobjective programming problems.

Abstract

The work being presented in the present thesis is devoted to the study of mixed symmetric duality in multiobjective programming problems under generalized convexity assumption. In the first chapter of the dissertation, nonlinear and multiobjective programming problem is introduced. The brief description of basic concepts, definitions that are used throughout work and detailed review of duality in single and multiobjective programming problems and summary of the thesis has also been discussed in this chapter. In chapter 2, we have reviewed a new pair of multiobjective second-order symmetric dual programs over arbitrary cones considered by Gupta et al. [20]and established weak, strong, converse and self duality theorems under K-\eta-bonvexity assumptions. In chapter 3, we have reviewed a pair of second-order mixed symmetric nondifferentiable multiobjective dual programs over arbitrary cones considered by Gupta et al. [19] and established weak, strong and converse duality theorems under K-(F; \rho)-convexity assumptions. In chapter 4, we have discussed higher order mixed multiobjective symmetric duality and prove weak duality theorem.