References
- Aboussoror A, Adly S, Saissi FE. A duality approach for a class of semivectorial bilevel programming problems. Vietnam J Math. 2018;46:197–214. doi: https://doi.org/10.1007/s10013-017-0268-5
- Babbahadda H, Gadhi N. Necessary optimality conditions for bilevel optimization problems using convexificators. J Glob Optim. 2006;34:535–549. doi: https://doi.org/10.1007/s10898-005-1650-5
- Bard JF. Some properities of the bilevel programming problem. J Optim Theory Appl. 1991;68:371–378. doi: https://doi.org/10.1007/BF00941574
- Chen Y, Florian M. On the geometry structure of linear Bilevel Programs: a dual approach. Montreal: Centre de Recherche sur les transports, Université de Montreal; 1992. (Technical Report CRT-867).
- Dempe S. A necessary and a sufficient optimality condition for bilevel programming problem. Optimization. 1992;25:341–354. doi: https://doi.org/10.1080/02331939208843831
- Dempe S. First-order necessary optimality conditions for general bilevel programming problems. J Optim Theory Appl. 1997;95:735–739. doi: https://doi.org/10.1023/A:1022646611097
- Dempe S, Dutta J, Mordukhovich BS. Necessary optimality conditions in optimistic bilevel programming. J Math Program Oper Res. 2010;56:577–604.
- Dempe S, Gadhi N, Zemkoho AB. New optimality conditions for the semivectorial bilevel optimization problem. J Optim Theory Appl. 2013;157:54–74. doi: https://doi.org/10.1007/s10957-012-0161-z
- Eichfelder G. Multiobjective bilevel optimization. Math Program. 2010;123:419–449. doi: https://doi.org/10.1007/s10107-008-0259-0
- Wang S, Wang Q, Romano-Rodriguez S. Optimality conditions and an algorithm for linear-quadratic bilevel programs. Optimization. 1993;4:521–536.
- Ye JJ. Constraint qualification and KKT conditions for bilevel programming problems. Math Oper Res. 2006;31:811–824. doi: https://doi.org/10.1287/moor.1060.0219
- Jourani A, Thibault L. Approximations and metric regularity in mathematical programming in Banach spaces. Math Oper Res. 1993;18:390–401. doi: https://doi.org/10.1287/moor.18.2.390
- Demyanov VF, Jeyakumar V. Huntting for a smaller convex subdifferential. J Optim Theory Appl. 1997;10:305–326.
- Dutta J, Chandra S. Convexificators, generalized convexity and optimality conditions. J Optim Theory Appl. 2002;113:41–65. doi: https://doi.org/10.1023/A:1014853129484
- Jeyakumar V, Luc DT, Schaible S. Characterizations of generalized monotone nonsmooth continuous maps using approximate Jacobians. J Convex Anal. 1998;5:119–132.
- Jeyakumar V, Tuan HD. Approximate Jacobian based nonsmooth Newton methods: convergence analysis. To appear.
- Khanh PQ, Dinh Tuan N. First and second order optimality conditions using approximations for nonsmooth vector optimization in Banach spaces. J Optim Theory Appl. 2006;130:289–308. doi: https://doi.org/10.1007/s10957-006-9103-y
- Amahroq T, Gadhi N. On the regularity condition for vector programming problems. J Glob Optim. 2001;21:435–443. doi: https://doi.org/10.1023/A:1012748412618
- Allali K, Amahroq T. Second order approximations and primal and dual necessary optimality conditions. Optimization. 1997;3:229–246. doi: https://doi.org/10.1080/02331939708844311
- Mordukhovich BS, Shao Y. On nonconvex subdifferential calculus in Banach spaces. J Convex Anal. 1995;0:211–227.
- Ioffe AD. Approximate subdifferential and applications, III: the metric theory. Mathematica. 1989;36:1–38.
- Loewen PD. Limits of Fréchet normals in nonsmooth analysis. Optimization nonlinear analysis. Pitman research notes mathematics series. 1992;244:178–188.
- Jeyakumar V, Luc DT. Nonsmooth calculus, minimality, and monotonicity of convexiflcators. J Optim Theory Appl. 1999;101:599–621. doi: https://doi.org/10.1023/A:1021790120780
- Khanh PQ, Dinh Tuan N. First and second-order approximations as derivatives of mappings in optimality conditions for nonsmooth vector optimization. Appl Math Optim. 2008;58:147–166. doi: https://doi.org/10.1007/s00245-008-9049-6
- Lafhim L, Gadhi N, Hamdaoui K, Rahou F. Necessary optimality conditions for a bilevel multiobjective programming problem via a Ψ-reformulation. Optimization. 2018;67:1–11. doi: https://doi.org/10.1080/02331934.2018.1523402
- Gadhi N. Optimality conditions and duality theorems for nonlipschitz optimization problems. Port Math. 2004;61:317–327.