On some aspects of multi objective mathematical programming

Abstract

The thesis comprises seven chapters and the gist of each chapter is given below: newlineThe first chapter is an introductory one and contains a brief survey of related literatures, preliminaries and summary of the research work presented in the thesis. newlineIn the second chapter, we derive optimality conditions for a non differentiable multi objective programming problem containing a square root of a certain quadratic form in each component of the objective function in the presence of equality and inequality constraints. As an application of Karush-Kuhn-Tucker type optimality conditions, a Mond-Weir type dual to this problem is formulated and various duality results are established under generalized invexity assumptions. Finally, a special case is deduced from our result. newlineIn the third chapter, Fritz John type optimality conditions for a multi objective variational problems with equality and inequality constraints are derived by an application of Karush -Kuhn-Tucker type optimality conditions, a Wolfe type second- order dual to this problem is formulated and various duality results are proved under generalized second-order invexity assumptions. A pair of Wolfe type second-order dual multi objective with natural boundary values is also presented to investigate duality. Finally, it is pointed out that our duality results established in this research can viewed as dynamic generalizations of those of static cases already existing in the literature. newlineIn the fourth chapter is composed two parts. In the first part, Fritz John and Karush-Kuhn-Tucker type optimality conditions for a class of non differentiable multi objective variational problems containing a term of square root of quadratic form in each of component of the vector functional are derived. As an application of Karush-Kuhn-Tucker type optimality conditions, a Mond-weir type second-order differentiable multiobjective dual variational problem is constructed. Various duality results for the pair of Mond-Weir type second- order dual variational.