We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush–Kuhn–Tucker type are established under the second-order constraint qualification. An application to Mond–Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.
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DOI : 10.1051/ro/2021039
Keywords: Asymptotic contingent epiderivative, optimality conditions, Karush–Kuhn–Tucker multiplier, constraint qualification, duality
@article{RO_2021__55_2_841_0,
author = {Tung, Nguyen Minh},
title = {Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives},
journal = {RAIRO. Operations Research},
pages = {841--860},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {2},
doi = {10.1051/ro/2021039},
mrnumber = {4243967},
zbl = {1475.90074},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021039/}
}
TY - JOUR AU - Tung, Nguyen Minh TI - Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives JO - RAIRO. Operations Research PY - 2021 SP - 841 EP - 860 VL - 55 IS - 2 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021039/ DO - 10.1051/ro/2021039 LA - en ID - RO_2021__55_2_841_0 ER -
%0 Journal Article %A Tung, Nguyen Minh %T Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives %J RAIRO. Operations Research %D 2021 %P 841-860 %V 55 %N 2 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021039/ %R 10.1051/ro/2021039 %G en %F RO_2021__55_2_841_0
Tung, Nguyen Minh. Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives. RAIRO. Operations Research, Tome 55 (2021) no. 2, pp. 841-860. doi: 10.1051/ro/2021039
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Dedicated to Professor Phan Quoc Khanh on the Occasion of his 75th birthday
