20 research outputs found
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
Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems
This paper is devoted to the study of nonsmooth generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be locally Lipschitz. We introduce a constraint qualification which is based on the Mordukhovich subdifferential. Then, we derive a Fritz-John type necessary optimality condition. Finally, interrelations between the new and the existing constraint qualifications such as the Mangasarian-Fromovitz, linear independent, and the Slater are investigated.Generalized semi-infinite programming Mordukhovich subdifferential Constraint qualification Lagrangian Optimality condition Nonsmooth optimization