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A Frank–Wolfe based branch-and-bound algorithm for mean-risk optimization

Author

Listed:
  • Christoph Buchheim

    (TU Dortmund)

  • Marianna De Santis

    (Università di Roma “La Sapienza”)

  • Francesco Rinaldi

    (Università di Padova)

  • Long Trieu

    (TU Dortmund)

Abstract

We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems by designing a branch-and-bound algorithm, where at each node, the continuous relaxation is solved by a non-monotone Frank–Wolfe type algorithm with away-steps. Experimental results on portfolio optimization problems show that our approach can outperform the MISOCP solver of CPLEX 12.6 for instances where a linear risk-weighting function is considered.

Suggested Citation

  • Christoph Buchheim & Marianna De Santis & Francesco Rinaldi & Long Trieu, 2018. "A Frank–Wolfe based branch-and-bound algorithm for mean-risk optimization," Journal of Global Optimization, Springer, vol. 70(3), pages 625-644, March.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:3:d:10.1007_s10898-017-0571-4
    DOI: 10.1007/s10898-017-0571-4
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    References listed on IDEAS

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    1. Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2013. "A new method for mean-variance portfolio optimization with cardinality constraints," Annals of Operations Research, Springer, vol. 205(1), pages 213-234, May.
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