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.
Keywords: Set-valued optimization, sharp minimizers, oriented distance function, sharp Fritz-John multipliers, sharp Karush–Kuhn–Tucker multipliers, optimality conditions
@article{RO_2022__56_2_619_0,
author = {Oussarhan, Abdessamad and Amahroq, Tijani},
title = {Sharp {Lagrange} multipliers for set-valued optimization problems},
journal = {RAIRO. Operations Research},
pages = {619--635},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {2},
doi = {10.1051/ro/2022034},
mrnumber = {4407589},
zbl = {1487.49017},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022034/}
}
TY - JOUR AU - Oussarhan, Abdessamad AU - Amahroq, Tijani TI - Sharp Lagrange multipliers for set-valued optimization problems JO - RAIRO. Operations Research PY - 2022 SP - 619 EP - 635 VL - 56 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022034/ DO - 10.1051/ro/2022034 LA - en ID - RO_2022__56_2_619_0 ER -
%0 Journal Article %A Oussarhan, Abdessamad %A Amahroq, Tijani %T Sharp Lagrange multipliers for set-valued optimization problems %J RAIRO. Operations Research %D 2022 %P 619-635 %V 56 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022034/ %R 10.1051/ro/2022034 %G en %F RO_2022__56_2_619_0
Oussarhan, Abdessamad; Amahroq, Tijani. Sharp Lagrange multipliers for set-valued optimization problems. RAIRO. Operations Research, Tome 56 (2022) no. 2, pp. 619-635. doi: 10.1051/ro/2022034
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