Abstract
In this chapter, we consider a mixed-integer bilevel linear programming problem with one parameter in the right-hand side of the constraints in the lower level (or, the follower’s) problem. Motivated by an application to the fuzzy portfolio optimization model, we consider a particular case that consists in maximizing the investor’s expected return. The functions are linear at both the upper and lower levels, and the proposed algorithm is based upon an approximation of the optimal value function using the branch-and-bound method. Therefore, at every node of this tree-type structure, we apply a new branch-and-bound procedure to deal with the integrity restriction.
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Acknowledgment
The research activity of the first author was partially funded by the R&D Department of the Tecnológico de Monterrey (ITESM), Campus Monterrey, Mexico, and by the SEP-CONACYT grant CB-2013-01-221676 (Mexico), while the second and third authors were financially supported by the SEP-CONACYT grant FC-2016-01-1938 (Mexico).
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Kalashnikov, V., Kalashnykova, N., Flores-Muñiz, J.G. (2018). Solution of the Portfolio Optimization Model as a Fuzzy Bilevel Programming Problem. In: Gil-Lafuente, A., Merigó, J., Dass, B., Verma, R. (eds) Applied Mathematics and Computational Intelligence. FIM 2015. Advances in Intelligent Systems and Computing, vol 730. Springer, Cham. https://doi.org/10.1007/978-3-319-75792-6_14
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