Výsledky vyhledávání - "J C, DICKINSON"

The extreme rays of the $$6\times 6$$ copositive cone

Autor: Peter J. C. Dickinson, Roland Hildebrand, Andrey Afonin

Publikováno v: Journal of Global Optimization. 79:153-190

We provide a complete classification of the extreme rays of the $$6 \times 6$$ copositive cone $$\mathcal {COP}^{6}$$ . We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix $$A

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::92a03e20baa5052199be877abfee9105
https://doi.org/10.1007/s10898-020-00930-y

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Generating irreducible copositive matrices using the stable set problem

Autor: Reinier de Zeeuw, Peter J. C. Dickinson

Publikováno v: Discrete applied mathematics, 296, 103-117. Elsevier

In this paper it is considered how graphs can be used to generate copositive matrices, and necessary and sufficient conditions are given for these generated matrices to then be irreducible with respect to the set of positive semidefinite plus nonnega

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0a392f66861ac90e090c0cd26e6df514
https://research.utwente.nl/en/publications/94d3d29e-1658-4271-82fa-3c3ab0edf10d

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Erratum to: On the DJL conjecture for order 6

Autor: Peter J. C. Dickinson

Publikováno v: Operators and matrices, 11(4), 1197-1200. Element d.o.o.

In this note an erratum is provided to the article “On the DJL conjecture for order 6” by Naomi Shaked-Monderer, published in Operators and Matrices 11(1), 2017, 71–88. We will demonstrate and correct two errors in this article. The first error

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https://doi.org/10.7153/oam-2017-11-81

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Notoriously hard (mixed-)binary QPs: empirical evidence on new completely positive approaches

Autor: Jia Liu, Abdel Lisser, Peter J. C. Dickinson, Jianqiang Cheng, Immanuel M. Bomze

Publikováno v: Computational Management Science, 16. Springer
Computational Management Science
Computational Management Science, Springer Verlag, 2019, 16 (4), pp.593-619. ⟨10.1007/s10287-018-0337-6⟩

By now, many copositive reformulations of mixed-binary QPs have been discussed, triggered by Burer’s seminal characterization from 2009. In conic optimization, it is very common to use approximation hierarchies based on positive-semidefinite (psd)

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::665da7a5f2651484720642c290bdac36
https://research.utwente.nl/en/publications/c8c30bf4-d616-48cd-9d8b-f7f324290c3a

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A new approximation hierarchy for polynomial conic optimization

Autor: Janez Povh, Peter J. C. Dickinson

Publikováno v: Computational optimization and applications, 73(1), 37-67. Springer
Computational optimization and applications, 73(1), 37-67. SPRINGER

In this paper we consider polynomial conic optimization problems, where the feasible set is defined by constraints in the form of given polynomial vectors belonging to given nonempty closed convex cones, and we assume that all the feasible solutions

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b9ccac2145c54ff3b228a3a115ddd02a
https://research.utwente.nl/en/publications/537d95f3-7b0d-49e9-b110-a67657d2eb06

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The structure of completely positive matrices according to their CP-rank and CP-plus-rank

Autor: Peter J. C. Dickinson, Georg Still, Immanuel M. Bomze

Publikováno v: Linear algebra and its applications, 482, 191-206. Elsevier

We study the topological properties of the cp-rank operator $\mathrm{cp}(A)$ and the related cp-plus-rank operator $\mathrm{cp}^+(A)$ (which is introduced in this paper) in the set $\mathcal{S}^n$ of symmetric $n\times n$-matrices. For the set of com

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0dddee727409e97ac40970bdb6ffc309
https://doi.org/10.1016/j.laa.2015.05.021

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A fresh CP look at mixed-binary QPs: new formulations and relaxations

Autor: Jianqiang Cheng, Abdel Lisser, Immanuel M. Bomze, Peter J. C. Dickinson

Publikováno v: Mathematical Programming
Mathematical Programming, Springer Verlag, 2017, 166 (1-2), pp.159-184. ⟨10.1007/s10107-017-1109-8⟩
Mathematical programming, 166(1-2), 159-184. Springer

Triggered by Burer’s seminal characterization from 2009, many copositive reformulations of mixed-binary QPs have been discussed by now. Most of them can be used as proper relaxations, if the intractable co(mpletely)positive cones are replaced by tr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d07d8cc8aa165144e991ea79318fbdcb
https://hal.archives-ouvertes.fr/hal-01775995

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Moment Approximations for Set-Semidefinite Polynomials

Autor: Peter J. C. Dickinson, Janez Povh

Publikováno v: Journal of optimization theory and applications, 159(1), 57-68. SPRINGER/PLENUM PUBLISHERS

The set of polynomials that are nonnegative over a subset of the nonnegative orthant (we call them set-semidefinite) have many uses in optimization. A common example of this type set is the set of copositive matrices, where we are effectively conside

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https://research.rug.nl/en/publications/c27c3087-0e44-43a3-be94-6e5a65ec11b6

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On the computational complexity of membership problems for the completely positive cone and its dual

Autor: Luuk Gijben, Peter J. C. Dickinson

Publikováno v: Computational optimization and applications, 57(2), 403-415. Springer

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi (Math. Program. 39(2):117---129, 1987) that the strong membership problem for the copositive cone, that

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https://doi.org/10.1007/s10589-013-9594-z

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Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets

Autor: Peter J. C. Dickinson, Gabriele Eichfelder, Janez Povh

Publikováno v: Optimization Letters. 7:1387-1397

In the paper we prove that any nonconvex quadratic problem over some set K µR n with additional linear and binary constraints can be rewritten as linear problem over the cone, dual to the cone of K-semidefinite matrices.

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https://doi.org/10.1007/s11590-013-0645-2

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