Conditionally definite matrices

Икрамов, Х. Д.; Savel'eva, N. V.

doi:10.1007/bf02355379

Cited by 34 publications

(12 citation statements)

References 32 publications

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“…Let (z,t,r) be the unique solution to the maximization problem (20)(21)(22)(23). In view of the symmetry property (24), it follows thatz = 0 n−1 , in which caset = 1.…”

Section: Theorem 211mentioning

confidence: 99%

Inradius and Circumradius of Various Convex Cones Arising in Applications

Henrion

Seeger

2010

Set-Valued Anal

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“…Let (z,t,r) be the unique solution to the maximization problem (20)(21)(22)(23). In view of the symmetry property (24), it follows thatz = 0 n−1 , in which caset = 1.…”

Section: Theorem 211mentioning

confidence: 99%

Inradius and Circumradius of Various Convex Cones Arising in Applications

Henrion

Seeger

2010

Set-Valued Anal

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“…While the time may not yet be ripe for writing up the final standard text book in this domain, several authors nonetheless bravely took the challenge of providing an overview, thereby aiming at a rapidly moving target. A recent survey on copositive optimization is offered by [57], while [77] and [74] provide reviews on copositivity with less emphasis on optimization. Bomze [16] and Busygin [37] provided entries in the most recent edition of the Encyclopedia of Optimization.…”

Section: Surveys Reviews Entries Book Chaptersmentioning

confidence: 99%

Copositive optimization – Recent developments and applications

Bomze

2012

European Journal of Operational Research

135

117

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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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“…Since then, numerous papers on both copositivity and complete positivity have emerged in the linear algebra literature, see [6] or [36] for surveys. Using these cones in optimization has been studied only in the last decade.…”

Section: Historical Remarksmentioning

confidence: 99%

“…Many conditions of the same flavor can be found in the literature. Again, it seems doubtful whether those conditions will prove useful for optimization purposes, so we refer to the surveys [33] and [36] for a more thorough treatment.…”

Section: Copositivity Criteria Based On Structural Matrix Propertiesmentioning

confidence: 99%

Copositive Programming – a Survey

Dür

2010

Recent Advances in Optimization and Its Applications in Engineering

179

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Copositive programming is a relatively young field in mathematical optimization. It can be seen as a generalization of semidefinite programming, since it means optimizing over the cone of so called copositive matrices. Like semidefinite programming, it has proved particularly useful in combinatorial and quadratic optimization. The purpose of this survey is to introduce the field to interested readers in the optimization community who wish to get an understanding of the basic concepts and recent developments in copositive programming, including modeling issues and applications, the connection to semidefinite programming and sum-of-squares approaches, as well as algorithmic solution approaches for copositive programs.

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Conditionally definite matrices

Cited by 34 publications

References 32 publications

Inradius and Circumradius of Various Convex Cones Arising in Applications

Inradius and Circumradius of Various Convex Cones Arising in Applications

Copositive optimization – Recent developments and applications

Copositive Programming – a Survey

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