Duality in mathematical programming.

In this thesis entitled, “Duality in Mathematical Programming”, the emphasis is given on formulation and conceptualization of the concepts of second-order duality, second-order mixed duality, second-order symmetric duality in a variety of nondifferentiable nonlinear programming under suitable second-order convexity/second-order invexity and generalized second-order convexity / generalized second-order invexity. Throughout the thesis nondifferentiablity occurs due to square root function and support functions. A support function which is more general than square root of a positive definite quadratic form. This thesis also addresses second-order duality in variational problems under suitable second-order invexity/secondorder generalized invexity. The duality results obtained for the variational problems are shown to be a dynamic generalization for thesis of nonlinear programming problem.Digital copy of Thesis.University of Kashmir

Some contributions to optimality criteria and duality in Multiobjective mathematical programming.

This thesis entitled, “some contributions to optimality criteria and duality in multiobjective mathematical programming”, offers an extensive study on optimality, duality and mixed duality in a variety of multiobjective mathematical programming that includes nondifferentiable nonlinear programming, variational problems containing square roots of a certain quadratic forms and support functions which are prominent nondifferentiable convex functions. This thesis also deals with optimality, duality and mixed duality for differentiable and nondifferentiable variational problems involving higher order derivatives, and presents a close relationship between the results of continuous programming problems through the problems with natural boundary conditions between results of their counter parts in nonlinear programming. Finally it formulates a pair of mixed symmetric and self dual differentiable variational problems and gives the validation of various duality results under appropriate invexity and generalized invexity hypotheses. These results are further extended to a nondifferentiable case that involves support functions.Digital copy of Thesis.University of Kashmir