Volume 56, Number 2, March-April 2022
|Page(s)||619 - 635|
|Published online||14 April 2022|
Sharp Lagrange multipliers for set-valued optimization problems
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: email@example.com.
Accepted: 25 February 2022
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.
Mathematics Subject Classification: 49J53 / 54C60 / 90C25 / 90C29
Key words: Set-valued optimization / sharp minimizers / oriented distance function / sharp Fritz-John multipliers / sharp Karush–Kuhn–Tucker multipliers / optimality conditions
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
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