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
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
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
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.