Study of Nonsmooth Cases in Nonlinear Programming Problems

Abstract

We have considered the minimization of a generalized Pareto problem defined on complete normed spaces. We will derive sufficient optimality conditions for generalized Pareto minimization problem. Some results on weak and strong duality will be derived. newlineWe have considered the minimization of a class of nondifferentiable pseudolinear functions over a closed and convex set subject to linear inequality constraints. The properties of locally Lipschitz pseudolinear functions will be used to establish several Lagrange multiplier characterizations of the solution set of the minimization problem. We will also derive certain conditions, under which an efficient solution becomes a properly efficient solution of a constrained nondifferentiable minimization problem. newlineWe have considered the nondifferentiable multi-objective minimization problem involving generalized Type I vector valued functions. We will derive Karush-Kuhn-Tucker type necessary and sufficient optimality conditions for a feasible solution to be an efficient or properly efficient solution. We will also derive various duality results for Wolfe type and Mond-Weir type duals under the generalized Type I assumptions. newline