Necessary and sufficient optimality conditions for set-valued optimization problems
Najia Benkenza, Nazih Abderrazzak Gadhi, Lahoussine Lafhim · Georgian Mathematical Journal · 2011
Abstract Using a special scalarization employed for the first time for the study of necessary optimality conditions in vector optimization by Ciligot-Travain [Numer. Funct. Anal. Optim. 15: 689–693, 1994], we give necessary optimality conditions for a set-valued optimization problem by establishing the existence of Lagrange–Fritz–John multipliers. Also, sufficient optimality conditions are given without any Lipschitz assumption.