Semidefinite relaxations for non-convex quadratic mixed-integer programming
We present semidefinite relaxations for unconstrained non-convex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for medium-sized instances, even if some of the variables are integer and unbounded. In this case, the problem co...
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| Vydané v: | Mathematical programming Ročník 141; číslo 1-2; s. 435 - 452 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2013
Springer Nature B.V |
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| ISSN: | 0025-5610, 1436-4646 |
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| Abstract | We present semidefinite relaxations for unconstrained non-convex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for medium-sized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We use this approach as a bounding routine in an SDP-based branch-and-bound framework. In case of a convex objective function, the new SDP bound improves the bound given by the continuous relaxation of the problem. Numerical experiments show that our algorithm performs well on various types of non-convex instances. |
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| AbstractList | We present semidefinite relaxations for unconstrained non-convex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for medium-sized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We use this approach as a bounding routine in an SDP-based branch-and-bound framework. In case of a convex objective function, the new SDP bound improves the bound given by the continuous relaxation of the problem. Numerical experiments show that our algorithm performs well on various types of non-convex instances. We present semidefinite relaxations for unconstrained non-convex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computationally easy to solve for medium-sized instances, even if some of the variables are integer and unbounded. In this case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We use this approach as a bounding routine in an SDP-based branch-and-bound framework. In case of a convex objective function, the new SDP bound improves the bound given by the continuous relaxation of the problem. Numerical experiments show that our algorithm performs well on various types of non-convex instances.[PUBLICATION ABSTRACT] |
| Author | Wiegele, Angelika Buchheim, Christoph |
| Author_xml | – sequence: 1 givenname: Christoph surname: Buchheim fullname: Buchheim, Christoph organization: Fakultät für Mathematik, Technische Universität Dortmund – sequence: 2 givenname: Angelika surname: Wiegele fullname: Wiegele, Angelika email: angelika.wiegele@aau.at organization: Institut für Mathematik, Alpen-Adria-Universität Klagenfurt |
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| Cites_doi | 10.1145/227683.227684 10.1007/s10898-008-9372-0 10.1007/BF00138689 10.1007/s10107-010-0371-9 10.1007/978-1-4757-4388-3 10.1007/s10107-004-0550-7 10.1016/j.disopt.2006.10.011 10.1007/s10107-008-0235-8 10.1007/BF01580665 10.1016/j.ejor.2008.01.054 10.1007/s10589-006-6448-y 10.1080/10556789908805765 10.1007/s12532-010-0010-8 10.1137/1038003 10.1007/978-1-4614-1927-3_14 10.1007/s10107-011-0475-x |
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