Bilevel programs

Bonnel , Optimality conditions for the semivectorial bilevel optimization problem, Pacific Journal of Optimization , 2 , Bonnel , L. Dempe and P. Mehlitz , Semivectorial bilevel programming versus scalar bilevel programming, Optimization , 69 , Dempe , N. Gadhi and A. Eichfelder , Multiobjective bilevel optimization, Mathematical Programming , , Wan and X. Zhao , Optimality conditions for bilevel optimization problem with both levels problems being multiobjective, Pacific Journal of Optimization , 13 , Li and Z.

Wan , On bilevel programs with a convex lower-level problem violating slater's constraint qualification, Journal of Optimization Theory and Applications , , Liu , Z. Wan , J. Chen and G. Lignola and J. Morgan , Topological existence and stability for stackelberg problems, Journal of Optimization Theory and Applications , 84 , Lv and Z.

Wan , Linear bilevel multiobjective optimization problem: penalty approach, Journal of Industrial and Management Optimization , 15 , Peng , J. Peng , X. Long and J. Yao , On the stability of solutions for semi-infinite vector optimization problems, Journal of Global Optimization , 70 , Tanino , Stability and sensitivity analysis in multiobjective nonlinear programming, Annals of Operations Research , 27 , Tanino and Y. Sawaragi , Stability of nondominated solutions in multicriteria decision-making, Journal of Optimization Theory and Applications , 30 , Wang , X.

Wang , Z. Wan and Y. Lv , A globally convergent algorithm for a class of bilevel nonlinear programming problem, Applied Mathematics and Computation , , Xiao , T.

Van and J. Yao , Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions, Positivity , 24 , Zhu and Q. Zhu , Exact penalization and necessary optimality conditions for generalized bilevel programming problems, SIAM Journal on Optimization , 7 , Ye , Nondifferentiable multiplier rules for optimization and bilevel optimization problems, SIAM Journal on Optimization , 15 , Yu , Essential weak efficient solution in multiobjective optimization problems, Journal of Mathematical Analysis and Applications , , Zhao , The lower semicontinuity of optimal solution sets, Journal of Mathematical Analysis and Applications , , Zheng , D.

Fang and Z. Wan , A solution approach to the weak linear bilevel programming problems, Optimization , 65 , Zheng and Z. Wan , A solution method for semivectorial bilevel programming problem via penalty method, Journal of Applied Mathematics and Computing , 37 , This is precisely what is done in the manually derived bilevel solution methods in bilevel example , but the possible benefit of using YALMIPs native support as we will do here is that this solver branches directly on the complementarity conditions, and thus avoids to introduce any numerically dangerous big-M constants.

Let us start with a simple bilevel linear programming problem. Hence, to obtain the final solution, we use value. Adding additional complicating constraints is allowed, as long as YALMIP can identify a solver which is capable of solving the outer problem appended with the KKT conditions, excluding the nonconvex complementary slackness constraint.

Hence, we can add integrality constraints easily to our model. A strong feature of the built-in solver is that it builds upon the infrastructure in YALMIP, and easily hooks up to almost any kind of outer problem.

Hence, we can take the problem above, and append a semidefinite constraint to the outer problem. The only difference is that during the branching of the complementary conditions, semidefinite programs have to be solved in each node. View at: MathSciNet S. Dempe, B. Mordukhovich, and A. Dempe and J. Dewez, M. Labb, P. Marcotte, and G. Thi, T. Duc, and P. Vicente and P. Wiesemann, A. Tsoukalas, P. Kleniati, and B. View at: Google Scholar B. Bank, J.

Guddat, D. Klatte, B. Kummer, and K. Lucchetti, F. Mignanego, and G. Bracken and J. Candler and R. View at: Google Scholar L. Vicente, C. Floudas, and P. Floudas and P. Pardalos, Eds. View at: Google Scholar J. Shimizu, Y. Ishizuka, and J. Dempe and V. Kalashnikov, Eds. Migdalas, P. Pardalos, and P. Luo, J. Pang, and D. Outrata, M. Demiguel, M. Friedlander, F.

Nogales, and S. Leyffer, G. Robinson, Ed. Ralph and S. View at: Google Scholar S. Mordukhovich, Variational Analysis and Generalized Differentiation , vol. View at: MathSciNet R. Rockafellar and R. Ye and D. Dempe, J. Dutta, and B. Ishizuka and E. Mersha and S. Guddat, H. Hollatz, and B. View at: Google Scholar K. Dempe, V. Kalashnikov, and R.

Doane and D. View at: Google Scholar R. Nafidi, and R. View at: Google Scholar V. Kalashnikov and R. Keyaerts, L. Meeus, and W. View at: Google Scholar H. Tomasgard, F. Romo, M. Fodstad, and K. View at: Google Scholar C. Chebouba, F. Yalaoui, A. Smati, L. Amodeo, K. Younsi, and A. Kabirian and M. Gabriel, J. Zhuang, and S. Egging, S. Gabriel, F. Holz, and J. Arano and B.

Zozaya, Ed. Kalashnikov, and G. Kalashnikov, N. Kalashnykova, and G. Clute, Ed. Kalashnikov, G. Tomasgard, and N. Kall and S. Kalashnikov, T. Matis, and G. Matis, and N. Kalashnikov, S. Dempe, G.

Watada, J. Phillips-Wren, G. Jain, and R. Howlett, Eds. Watada, G. Phillips-Wren, L. View at: Google Scholar D. Kinderlehrer and G. View at: MathSciNet O. Nishimura, S. Hayashi, and M.

Saharidis and M. Lei, C. Guang-Nian, and L. Xu, Y. Tu, and Z. Fang, P. Guo, M. Li, and L. Hongli, L. Juntao, and G. Ho and S. Yin, S. Wong, N.

Sze, and H. Liang, J. Gao, and K. Wang and F. Burgard, P. Pharkya, and C. Calvete, C. Legillon, A. Liefooghe, and E. Cordero-Franco, and R. Huang and N. Feng and C. Wang, J. Zhu, J. Huang, and M. Sun, Z. Gao, and J. Xu and P. View at: Google Scholar P. Hansen, Y. Kochetov, and N. View at: Google Scholar I. Klimentova, and Y. View at: Google Scholar M. Bhadury, J. Jaramillo, and R.

Uno, H. Katagiri, and H. Marianov, M. Aras, and I. Kress and E. Aras, and K. Ashtiani, A. Makui, and R. Kim, J. Lee, and J. Lee, L. Song, and H. Brown, D.

Hankerson, J. Lopez, and A. Hong, S. Oh, and H. View at: Google Scholar A. Weimerskirch and C. Avanzi, E. Sava, and S. Moreno, J. Miret, and F. View at: Google Scholar N. Arroyo and F. Liu, J. Jung, G. Heydt, V. Vittal, and A. Roy, D. Kim, and K. Yuan, Z. Li, and K. View at: Publisher Site Google Scholar.