Necessary Conditions for Optimality of Decomposable Entanglement Witnesses

Necessary Optimality Conditions for Multiobjective Bilevel Programs

The multiobjective bilevel program is a sequence of two optimization problems, with the upper-level problem being multiobjective and the constraint region of the upper level problem being determined implicitly by the solution set to the lower-level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of all lower-level problems near...

Necessary optimality conditions for discrete inclusions

The aim of this paper is to present a short survey of several new results concerning optimization of discrete inclusions. We study an optimization problem given by a discrete inclusion with end point constraints and we present several approaches concerning first and secondorder necessary optimality conditions for this problem.

Spectral conditions for positive maps and entanglement witnesses

We provide partial classification of entanglement witnesses and positive maps which is based on a family of spectral conditions. Interestingly many well known examples of positive maps (e.g. transposition, reduction map, the family of Choi maps) belong to the class constructed via spectral conditions.

Necessary and Sucient Optimality Conditions for a Control Fuzzy Linear Problem

Necessary Optimality Conditions in Pessimistic Bilevel Programming Necessary Optimality Conditions in Pessimistic Bilevel Programming

This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipsch...