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

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....

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Bibliographic Details
Published inJournal of global optimization Vol. 70; no. 3; pp. 625 - 644
Main Authors Buchheim, Christoph, De Santis, Marianna, Rinaldi, Francesco, Trieu, Long
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2018
Springer
Springer Nature B.V
Subjects
Algorithms
Branch & bound algorithms
Computer Science
Continuity (mathematics)
Covariance matrix
Investment analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Risk
90C10
90C90
Global optimization
Mean-risk optimization
90C57
Mixed-integer programming
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Summary: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.
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-017-0571-4