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A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization

Christoph Buchheim (christoph.buchheim***at***tu-dortmund.de)
Marianna De Santis (marianna.desantis***at***aau.at)
Francesco Rinaldi (rinaldi***at***math.unipd.it)
Long Trieu (long.trieu***at***math.tu-dortmund.de)

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, portfolio optimization, global optimization

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )


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Entry Submitted: 07/21/2015
Entry Accepted: 07/21/2015
Entry Last Modified: 05/05/2017

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