Contributions to Duality in Mathematical Programming

Abstract

The thesis entitled, Contributions To Duality in Mathematical Programming is an outcome of research work carried out newlineby the author under the able guidance of Dr. I. Husain, professor, Department newlineof Mathematics, National Institute of Technology, Srinagar, Kashmir. newlineThe purpose of this thesis is to study optimality criteria, and duality and mixed duality in a variety of mathematical programming that includes non differentiable nonlinear programming, nondifferentiable nonlinear fractional programming, nondifferentiable minimax fractional programming, continuous - time minmax programming and variational problems. newlineThe thesis comprises seven chapters and each chapter is subdivided into two or more sections. newlineChapter 1 is an introductory one and contains a brief survey of related literatures and summary of the research work presented in this thesis. newlineChapter 2 is focused on nonlinear programming problems containing support functions. newlineIn chapter 3, Fritz John and Karush-Kuhn - Tucker type optimality conditions for a constrained variational problem involving higher order derivatives are obtained. As an application of these Karush-Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type duals are formulated, and newlinevarious duality relationships between the primal problem and each of the dual newlineproblems are established under invexity and generalized invexity. newlineChapter 4 is devoted to study optimality and duality and mixed type newlineduality in continuous programming problems containing support functions. newlineChapter 5 consists of two sections. In section 5.1 necessary sufficient optimality conditions for nondifferentiable minmax programming problems are derived and Mond - Weir type duality as well as Schaible type duality is investigated. Sec 5.2, deals with optimality and duality for continuous - newlinetime minimax programming problems. newlineChapter 6 has two sections. In section 6.1 mixed type symmetric and self duality for variational problems are studied