We consider Karush-Kuhn-Tucker (KKT) systems, which depend on a parameter. Our contribution concerns with the existence of solution of the directionally perturbed KKT system, approximating the given primaldual base solution. To our knowledge, we give the first explicit result of this kind in the situation where the multiplier associated with the base primal solution may not be unique. The condi...

In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinear program when the set Λ∗ of the Karush-Kuhn-Tucker multiplier vectors is empty owing to the fact that the constraint qualifications are not satisfied.

Abstract In this paper, for a nonsmooth semi-infinite multiobjective programming with locally Lipschitz data, some weak and strong Karush-KuhnTucker type optimality conditions are derived. The necessary conditions are proposed under a constraint qualification, and the sufficient conditions are explored under assumption of generalized invexity. All results are expressed in terms of Clarke subdif...

This paper studies first order conditions (Karush–Kuhn–Tucker conditions) for discretized optimal control problems with nonsmooth constraints. We present a simple condition which can be used to verify that a local optimal point satisfies the first order conditions and that a point satisfying the first order conditions is a global or local optimal solution of the optimal control problem.

This paper studies bilevel polynomial optimization. We propose a method to solve it globally by using optimization relaxations. Each relaxation is obtained from the Karush--Kuhn--Tucker ...

A new parameterized binary relation is used to define minimality concepts in vector optimization. To simplify the problem of determining minimal elements the method of scalarization is applied. Necessary and sufficient conditions for the existence of minimal elements with respect to the scalarized problems are given. The multiplier rule of Lagrange is generalized. As a necessary minimality cond...

In this paper, we give some new generalized convexities with the tool–right upper-Diniderivative which is an extension of directional derivative. Next, we establish not only Karush-KuhnTucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak ...

Abs t rac t -P roper t i e s of nonlinear multiobjective problems implied by the Karush-Kuhn-Tucker necessary conditions are investigated. It is shown that trajectories of Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of vector deviations in the balance space (to the balance set for Pareto solutions). ~) 2003 El...