V. V. Kalashnikov, N. I. Kalashnykova, M. A. LEAL-CORONADO


In this paper, we consider a mixed-integer bi-level linear programming (or a leader’s) problem with one parameter in the right-hand side of the constraints in the lower level (or a follower’s) problem. Motivated by the application to a fuzzy portfolio optimization model, we consider a particular case that consists in maximizing the investor’s expected return. The functions are linear at the upper level and quadratic at the lower level, 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 branch-and-bound structure, we apply a new branch-and-bound technique to process the integrity condition.


fuzzy portfolio optimization, integer programming, parametric programming, branch-and-bound approach.


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