Symmetric and non-symmetric duality in multiobjective programming problems

Abstract

The work being presented in the present thesis is devoted to the study of symmetric and non-symmetric duality results in multiobjective programming for some dual mathematical 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, defi nitions 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 pair of second-order Mond-Weir type symmetric duality in multiobjective programming problem considered by Suneja et al. [29] and established weak duality and strong duality under the assumption of n -bonvexity and n -pseudobonvexity. In chapter 3, we have studied a pair of higher order Wolfe and Mond-Weir type multiobjec- tive symmetric dual programs over arbitrary cones considered by [32] and the duality results are established under higher order (F;a ;b ; d)-convexity/pseudo-convexity assumptions. In chapter 4, motivated by Kim et al. [33], we have discussed Mond-Weir type higher order multiobjective dual involving the nondi erentiable function and cone constraints, where every component of the objective function contains a term involving the support function of a compact convex set and established weak, strong duality theorems under the assumption of Higher order (F;a ;b ; d) type-I.