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

Christoph Buchheim (), Marianna De Santis (), Francesco Rinaldi () and Long Trieu ()
Additional contact information
Christoph Buchheim: TU Dortmund
Marianna De Santis: Università di Roma “La Sapienza”
Francesco Rinaldi: Università di Padova
Long Trieu: TU Dortmund

Journal of Global Optimization, 2018, vol. 70, issue 3, No 6, 625-644

Abstract: 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.

Keywords: Mixed-integer programming; Mean-risk optimization; Global optimization; 90C10; 90C57; 90C90 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-017-0571-4

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