Articles

Please contact me (peter.jc.dickinson@gmail.com) if you want a copy of any of my articles.

More details on my papers are available at google scholar.

Miscellaneous publications

Peter J.C. Dickinson. The Copositive Cone, the Completely Positive Cone and their Generalisations. PhD thesis, University of Groningen, 2013. (Cum Laude distinction, highest distinction possible at the University of Groningen.)
Peter J.C. Dickinson. The Copositive Cone. Nieuw Archief voor Wiskunde 15 (2014), Issue 4, 255-256. (An article in the quarterly journal of the Royal Dutch Mathematical Society introducing myself and my research.)

Submitted to international peer reviewed journals

Peter J.C. Dickinson. Generating irreducible copositive matrices using the stable set problem. (Preprint, Zipped file of all co-point-determing co-irreducible graphs on at most 13 vertices)
Andrey Afonin, Peter J.C. Dickinson and Roland Hildebrand. The extreme rays of the 6 x 6 copositive cone.

Published in international peer reviewed journals

Peter J.C. Dickinson and Janez Povh. A new approximation hierarchy for polynomial conic optimization. Computational Optimization and Applications 73 (2019), Issue 1, 37-67.
Peter J.C. Dickinson. A new certificate for copositivity. Linear Algebra and its Applications 569 (2019), 15-37.
Immanuel M. Bomze, Jianqiang Cheng, Peter J. C. Dickinson, Abdel Lisser and Jia Liu. Notoriously hard (mixed-)binary QPs: empirical evidence on new completely positive approaches. Computational Management Science 16 (2019), 593-619.
Peter J.C. Dickinson. Erratum to: On the DJL conjecture for order 6. Operators and Matrices 11 (2017), Issue 4, 1197-1200.
Immanuel Bomze, Jianqiang Cheng, Peter J.C. Dickinson and Abdel Lisser. A fresh CP look at mixed-binary QPs: New formulations and relaxations. Mathematical Programming 166 (2017), Issue 1-2, 159-184.
Peter J.C. Dickinson and Roland Hildebrand. Considering Copositivity Locally. Journal of Mathematical Analysis and Applications 437 (2016), Issue 2, 1184-1195.
Immanuel Bomze, Peter J.C. Dickinson and Georg Still. The structure of completely positive matrices according to their CP-rank and CP-plus-rank. Linear Algebra and its Applications 482 (2015), 191-206.
Peter J.C. Dickinson and Janez Povh. On an extension of Pólya's Positivstellensatz. Journal of Global Optimization. 61 (2015), Issue 4, 615-625. (Recognised as one of the "Top-5 Papers Published in Journal of Global Optimization in 2015".)
Peter J.C. Dickinson and Luuk Gijben. On the Computational Complexity of Membership Problems for the Completely Positive Cone and its Dual. Computational Optimization and Applications 57 (2014), Issue 2, 403-415.
Peter J.C. Dickinson. On the Exhaustivity of Simplicial Partitioning. Journal of Global Optimization 58 (2014), Issue 1, 189-203.
Peter J.C. Dickinson and Janez Povh. Moment approximations for set-semidefinite polynomials. Journal of Optimization Theory and Applications 159 (2013), Issue 1, 57-68.
Peter J.C. Dickinson, Mirjam Dür, Luuk Gijben and Roland Hildebrand. Scaling relationship between the copositive cone and Parrilo's first level approximation. Optimization Letters 7 (2013), Issue 8, 1669-1679. (Received the 2013 OPTL Best Paper Award.)
Peter J.C. Dickinson, Mirjam Dür, Luuk Gijben and Roland Hildebrand. Irreducible elements of the copositive cone. Linear Algebra and its Applications 439 (2013), Issue 6, 1605-1626.
Peter J.C. Dickinson, Gabriele Eichfelder and Janez Povh. Erratum to: On the set-semidefinite representation of nonconvex quadratic programs over arbitrary feasible sets. Optimization Letters 7 (2013), Issue 6, 1387-1397.
Peter J.C. Dickinson and Mirjam Dür. Linear-time complete positivity detection and decomposition of sparse matrices. SIAM Journal On Matrix Analysis and Applications 33 (2012), Issue 3, 701-720.
Peter J.C. Dickinson. Geometry of the Copositive and Completely Positive Cones. Journal of Mathematical Analysis and Applications 380 (2011), Issue 1, 377-395.
Peter J.C. Dickinson. An improved characterisation of the interior of the completely positive cone. Electronic Journal of Linear Algebra 20 (2010), 723-729.

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