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: firstname.lastname@example.org.
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.