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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Published in:Journal of global optimization Vol. 70; no. 3; pp. 625 - 644
Main Authors: Buchheim, Christoph, De Santis, Marianna, Rinaldi, Francesco, Trieu, Long
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2018
Springer
Springer Nature B.V
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ISSN:0925-5001, 1573-2916
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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.
AbstractList 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.
Audience Academic
Author Rinaldi, Francesco
Buchheim, Christoph
De Santis, Marianna
Trieu, Long
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  givenname: Francesco
  surname: Rinaldi
  fullname: Rinaldi, Francesco
  organization: Dipartimento di Matematica, Università di Padova
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  givenname: Long
  surname: Trieu
  fullname: Trieu, Long
  organization: Fakultät für Mathematik, TU Dortmund
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Snippet 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...
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SubjectTerms Algorithms
Branch & bound algorithms
Computer Science
Continuity (mathematics)
Covariance matrix
Investment analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Risk
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Title A Frank–Wolfe based branch-and-bound algorithm for mean-risk optimization
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