Copositive optimization – Recent developments and applications
► Copositive optimization is an important problem class within conic optimization which receives much attention nowadays. ► It allows reformulation of diverse NP-hard problems, including nonconvex, mixed-binary, and fractional quadratic problems. ► Combinatorial applications: quadratic assignment, b...
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| Published in | European journal of operational research Vol. 216; no. 3; pp. 509 - 520 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.02.2012
Elsevier Elsevier Sequoia S.A |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-2217 1872-6860 |
| DOI | 10.1016/j.ejor.2011.04.026 |
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| Abstract | ► Copositive optimization is an important problem class within conic optimization which receives much attention nowadays. ► It allows reformulation of diverse NP-hard problems, including nonconvex, mixed-binary, and fractional quadratic problems. ► Combinatorial applications: quadratic assignment, bounding the clique and the crossing number, graph coloring and partitioning. ► Applications in the continuous domain: stability in switched systems, optimality conditions, and tight convex underestimation. ► Further applications: rigid body mechanics, networks in queueing, traffic, reliability, uncertainty in Q2 mixed-integer LPs.
Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile field of research. It is a special case of conic optimization, which consists of minimizing a linear function over a cone subject to linear constraints. The diversity of copositive formulations in different domains of optimization is impressive, since problem classes both in the continuous and discrete world, as well as both deterministic and stochastic models are covered. Copositivity appears in local and global optimality conditions for quadratic optimization, but can also yield tighter bounds for NP-hard combinatorial optimization problems. Here some of the recent success stories are told, along with principles, algorithms and applications. |
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| AbstractList | Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile field of research. It is a special case of conic optimization, which consists of minimizing a linear function over a cone subject to linear constraints. The diversity of copositive formulations in different domains of optimization is impressive, since problem classes both in the continuous and discrete world, as well as both deterministic and stochastic models are covered. Copositivity appears in local and global optimality conditions for quadratic optimization, but can also yield tighter bounds for NP-hard combinatorial optimization problems. Here some of the recent success stories are told, along with principles, algorithms and applications. [PUBLICATION ABSTRACT] ► Copositive optimization is an important problem class within conic optimization which receives much attention nowadays. ► It allows reformulation of diverse NP-hard problems, including nonconvex, mixed-binary, and fractional quadratic problems. ► Combinatorial applications: quadratic assignment, bounding the clique and the crossing number, graph coloring and partitioning. ► Applications in the continuous domain: stability in switched systems, optimality conditions, and tight convex underestimation. ► Further applications: rigid body mechanics, networks in queueing, traffic, reliability, uncertainty in Q2 mixed-integer LPs. Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile field of research. It is a special case of conic optimization, which consists of minimizing a linear function over a cone subject to linear constraints. The diversity of copositive formulations in different domains of optimization is impressive, since problem classes both in the continuous and discrete world, as well as both deterministic and stochastic models are covered. Copositivity appears in local and global optimality conditions for quadratic optimization, but can also yield tighter bounds for NP-hard combinatorial optimization problems. Here some of the recent success stories are told, along with principles, algorithms and applications. Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile field of research. It is a special case of conic optimization, which consists of minimizing a linear function over a cone subject to linear constraints. The diversity of copositive formulations in different domains of optimization is impressive, since problem classes both in the continuous and discrete world, as well as both deterministic and stochastic models are covered. Copositivity appears in local and global optimality conditions for quadratic optimization, but can also yield tighter bounds for NP-hard combinatorial optimization problems. Here some of the recent success stories are told, along with principles, algorithms and applications. |
| Author | Bomze, Immanuel M. |
| Author_xml | – sequence: 1 givenname: Immanuel M. surname: Bomze fullname: Bomze, Immanuel M. email: bomze.ejor@univie.ac.at organization: Department of Statistics and Operations Research, University of Vienna, Austria |
| BackLink | http://www.econis.eu/PPNSET?PPN=680050892$$DView this record in ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24624637$$DView record in Pascal Francis |
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| Keywords | Clique number Robust optimization Standard quadratic optimization Convexity gap Completely positive matrix Crossing number Stochastic model Cone conic programming Graph clique Local optimum Minimization Global optimum Combinatorial optimization Global local method Deterministic model NP hard problem Optimality condition Optimality criterion Convexity Mathematical programming |
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| Snippet | ► Copositive optimization is an important problem class within conic optimization which receives much attention nowadays. ► It allows reformulation of diverse... Due to its versatility, copositive optimization receives increasing interest in the Operational Research community, and is a rapidly expanding and fertile... |
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| SubjectTerms | Algorithms Applied sciences Clique number Combinatorial analysis Communities Completely positive matrix Computer science; control theory; systems Conics Convexity gap Crossing number Exact sciences and technology Flows in networks. Combinatorial problems Information retrieval. Graph Mathematical models Mathematical problems Operational research Operational research and scientific management Operational research. Management science Operations research Optimization Optimization algorithms Robust optimization Standard quadratic optimization Studies Theoretical computing Versatility |
| Title | Copositive optimization – Recent developments and applications |
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