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 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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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. |
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| 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 |
| Author_xml | – sequence: 1 givenname: Christoph surname: Buchheim fullname: Buchheim, Christoph organization: Fakultät für Mathematik, TU Dortmund – sequence: 2 givenname: Marianna surname: De Santis fullname: De Santis, Marianna email: mdesantis@dis.uniroma1.it organization: Dipartimento di ingegneria informatica, automatica e gestionale, Università di Roma “La Sapienza” – sequence: 3 givenname: Francesco surname: Rinaldi fullname: Rinaldi, Francesco organization: Dipartimento di Matematica, Università di Padova – sequence: 4 givenname: Long surname: Trieu fullname: Trieu, Long organization: Fakultät für Mathematik, TU Dortmund |
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| CitedBy_id | crossref_primary_10_1007_s10898_023_01271_2 crossref_primary_10_1007_s12532_019_00160_8 crossref_primary_10_3390_brainsci13060866 crossref_primary_10_1007_s12532_025_00288_w crossref_primary_10_3390_math13183038 crossref_primary_10_1016_j_orl_2022_04_007 |
| Cites_doi | 10.1023/A:1020587701058 10.1137/140978971 10.1002/nav.3800030109 10.1016/j.orl.2008.04.006 10.1007/BF01589445 10.1137/1.9781611971309 10.1145/1824777.1824783 10.1137/S1052623401399903 10.1007/s10479-012-1165-7 10.1137/0723046 10.1007/s101070100263 10.1007/BF00940345 10.1007/BF01580223 10.1137/0318035 10.1145/1068009.1068111 10.1007/s10107-014-0841-6 10.1007/978-3-319-14115-2_6 10.1145/1390156.1390191 |
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| DOI | 10.1007/s10898-017-0571-4 |
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| Keywords | 90C10 90C90 Global optimization Mean-risk optimization 90C57 Mixed-integer programming |
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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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