Sharp Lagrange multipliers for set-valued optimization problems

¹ LIMATI Laboratory, Sultan Moulay Slimane University, Poly-disciplinary Faculty, B.P. 592 Beni Mellal, Morocco
² LAMAI Laboratory, Cadi Ayyad University, Faculty of Sciences and Techniques, B.P. 549 Marrakech, Morocco

^* Corresponding author: abdessamad.oussa@gmail.com.

Received: 5 August 2021
Accepted: 25 February 2022

Abstract

In this paper, we give a comparison among some notions of weak sharp minima introduced in Amahroq et al. [Le matematiche J. 73 (2018) 99–114], Durea and Strugariu [Nonlinear Anal. 73 (2010) 2148–2157] and Zhu et al. [Set-Valued Var. Anal. 20 (2012) 637–666] for set-valued optimization problems. Besides, we establish sharp Lagrange multiplier rules for general constrained set-valued optimization problems involving new scalarization functionals based on the oriented distance function. Moreover, we provide sufficient optimality conditions for the considered problems without any convexity assumptions.