Optimality conditions of a set valued optimization problem with the help of directional convexificators
Nazih Abderrazzak Gadhi, Fatima Zahra Rahou, Mohammed El Idrissi, Lahoussine Lafhim · Optimization · 2020
Motivated by a work of Dempe and Pilecka [Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming. J Global Optim. 2015;61:769–788], where the authors introduced the notion of directional convexificators, we investigate a set valued optimization problem P. Using a scalarization technique by mean of the Hiriart-Urruty signed distance function, together with directional convexificators, we give necessary optimality conditions of (P). Sufficient optimality conditions are obtained under a new generalized convexity. To illustrate the obtained results, an example is given.