Geodesic
Combined Approach with Second-Order Optimality Conditions for Bilevel Programming Problems
Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1173-1201
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We propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by the combined approach developed by Ye and Zhu in 2010, where the authors combined the classical first-order and the value function approaches to derive new necessary optimality conditions. In our approach, we add a second-order optimality condition to the combined program as a new constraint. We show that when all known approaches fail, adding the second-order optimality condition as a constraint makes the corresponding partial calmness condition and the resulting necessary optimality condition easier to hold. We also give some discussions on advantages and disadvantages of the combined approaches with the first-order and the second-order information.
Classification : 90C26, 90C30, 90C31, 90C33, 90C46, 49J52, 91A65
Mots-clés : Partial calmness, bilevel program, optimality condition, second-order optimality condition 
@article{JCA_2023_30_4_JCA_2023_30_4_a4,
     author = {X. Ma and W. Yao and J. J. Ye and J. Zhang},
     title = {Combined {Approach} with {Second-Order} {Optimality} {Conditions} for {Bilevel} {Programming} {Problems}},
     journal = {Journal of convex analysis},
     pages = {1173--1201},
     year = {2023},
     volume = {30},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a4/}
}
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X. Ma; W. Yao; J. J. Ye; J. Zhang. Combined Approach with Second-Order Optimality Conditions for Bilevel Programming Problems. Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1173-1201. http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a4/