Sequential Optimality Conditions for Bilevel Multiobjective Fractional Programming Problems with Extremal Value Function
Subject Areas : Operation Research
1 - University Chouaib Doukkali
Keywords: convex, vetor, mappings,
Abstract :
In this paper, we consider a bilevel multiobjective fractional programming problem $(\mathcal{BMFP})$ with an extremal value function. We provide necessary and sufficient optimality conditions characterizing (properly, weakly) efficient solutions of the considered problem. These optimality conditions are obtained in terms of sequences and based on sequential calculus rules for the Br\o ndsted-Rockafellar subdifferential of the sum and the multi-composition of convex functions, without constraint qualifications.
Ahmad, I., Zhang, F., Liu, J. (2018). Anjum, M.N., Zaman, M., Tayyab, M., Waseem, M., Farid, H.U.: A linear bi-level multi-objective program for optimal allocation of water resources. Plos one 13(2), 1-25.
Aboussoror, A., Adly, S. (2011) A Fenchel-Lagrange duality approach for a bilevel programming problem with extremal-value function. J. Optim. Theory Appl. 149(2), 254-268.
Bard, J.F. (2013). Practical Bilevel Optimization: Algorithms and Applications, vol. 30. Springer Science & Business Media.
Bot, R.I., Vargyas, E., Wanka, G. (2007) Conjugate duality for multiobjective composed optimization problems. Acta Math. Hungarica 116(3), 177-196.
Bot, R.I., Grad, S.M., Wanka, G. (2009). Duality in Vector Optimization. Springer Science & Business Media.
Colson, B., Marcotte, P., Savard, G. (2007). An overview of bilevel optimization. Ann. Oper. Res. 153(1), 235-256.
Dempe, S. (2002). Foundations of Bilevel Programming. Springer Science & Business Media.
Dempe, S. (2015). Kalashnikov, V., Perez-Valdes, G.A., Kalashnykova, N.: Bilevel Programming Problems. Springer, Berlin, Heidelberg.
Eichfelder, G. (2010) Multiobjective bilevel optimization. Math. Program. 123(2), 419-449.
Floudas, C.A., (2009). Pardalos, P.M.: Encyclopedia of Optimization. Springer Science & Business Media.
Laghdir, M., Dali, I., Moustaid, M.B. (2020). A generalized sequential formula for subdi erential of multi-composed functions de ned on Banach spaces and applications. Pure Appl. Funct. Anal. 5(4), 999-1023.
Migdalas, A. (1995). Bilevel programming in traffic planning: Models, methods and challenge. J. Global Optim. 7(4), 38-405.
Stancu-Minasian, I.M. (2012). Fractional Programming: Theory, Methods and Applications, vol. 409. Springer Science & Business Media.
Stancu-Minasian, I.M., (2019) A ninth bibliography of fractional programming. Optimization 68(11), 2125-2169.
Shimizu, K., (2012), Ishizuka, Y., Bard, J.F.: Nondi erentiable and Two-level Mathematical Programming. Springer Science & Business Media.
Shimizu, K., Ishizuka, Y., (1985) Optimality conditions and algorithms for parameter design problems with two-level structure. IEEE Trans. Autom. Control 30(10), 986-993.
Thibault, L. (1995). A generalized sequential formula for subdi erentials of sums of convex functions de ned on Banach spaces. Lecture Notes Econom. Math. Syst.
Thibault, L. (1997). Sequential convex subdi erential calculus and sequential Lagrange multipliers. SIAM J. Control Optim.
Wang, H., Zhang, R. (2015). Duality for multiobjective bilevel programming roblems with extremal-value function. J. Math. Res. Appl. 35(3), 311-320.
Yin, Y. (2002). Multiobjective bilevel optimization for transportation planning and management problems. J. Adv. Transp. 36(1), 93-105.