Freire, A. S., Moreno, E., & Vielma, J. P. (2012). An integer linear programming approach for bilinear integer programming. Oper. Res. Lett., 40(2), 74–77.
Abstract: We introduce a new Integer Linear Programming (ILP) approach for solving Integer Programming (IP) problems with bilinear objectives and linear constraints. The approach relies on a series of ILP approximations of the bilinear P. We compare this approach with standard linearization techniques on random instances and a set of real-world product bundling problems. (C) 2011 Elsevier B.V. All rights reserved.
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Lagos, G., Espinoza, D., Moreno, E., & Vielma, J. P. (2015). Restricted risk measures and robust optimization. Eur. J. Oper. Res., 241(3), 771–782.
Abstract: In this paper we consider characterizations of the robust uncertainty sets associated with coherent and distortion risk measures. In this context we show that if we are willing to enforce the coherent or distortion axioms only on random variables that are affine or linear functions of the vector of random parameters, we may consider some new variants of the uncertainty sets determined by the classical characterizations. We also show that in the finite probability case these variants are simple transformations of the classical sets. Finally we present results of computational experiments that suggest that the risk measures associated with these new uncertainty sets can help mitigate estimation errors of the Conditional Value-at-Risk. (C) 2014 Elsevier B.V. All rights reserved.
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