Duality without constraint qualification in nonsmooth optimization

We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality results are obtained without a constraint qualification

Local cone approximations in mathematical programming

We show how to use intensively local cone approximations to obtain results in some fields of optimization theory as optimality conditions, constraint qualifications, mean value theorems and error bound

Optimality Criteria and Duality in Multiobjective Programming Involving Nonsmooth Invex Functions

Abstract. In this paper a generalization of invexity is considered in a general form, by means of the concept of K-directional derivative. Then in the case of nonlinear multiobjective programming problems where the functions involved are nondifferentiable, we established sufficient optimality conditions without any convexity assumption of the K-directional derivative. Then we obtained some duality results. Mathematics Subject Classification

Infine functions and nonsmooth multiobjective optimization problems

AbstractIn this paper, we consider notion of infine functions and we establish necessary and sufficient optimality conditions for a feasible solution of a multiobjective optimization problem involving mixed constraints (equality and inequality) to be an efficient or properly efficient solution. We also obtain duality theorems for Wolf type and Mond-Weir type duals under the generalized invexity assumptions

Convexificators and strong Kuhn–Tucker conditions

AbstractThis study is devoted to constraint qualifications and strong Kuhn–Tucker necessary optimality conditions for nonsmooth multiobjective optimization problems. The main tool of the study is the concept of convexificators. Mangasarian–Fromovitz type constraint qualification and several other qualifications are proposed and their relationships are investigated. In addition, sufficient optimality conditions are studied