My primary research interest is in Mathematical Optimisation, with the main focuses being on Continuous, Conic, Copositive and Polynomial Optimisation. I am also interested in Matrix Analysis.

Whilst at Cambridge I studied theoretical physics, being interested in the subject in general, rather than any specific areas. I tend to have at least a partial interest in anything and everything.

My Publons profile provides a verified summary of some of my previous refereeing duties.

My Google Scholar Citations homepage provides information on citations of my articles and formats for referencing my articles (e.g. bibtex).

My Erdös number is 4 (via 1: P.J. Cameron, 2: S. Severini, 3: R. Hildebrand or via 1: R.L. Graham, 2: P.M. Pardalos, 3: I.M. Bomze).

If you would like to obtain a copy of any of my papers, please send me an email.


    Submitted to international peer reviewed journals

  1. Peter J.C. Dickinson:
    A New Certificate For Copositivity.
    (Preprint, Matlab code)
  2. Peter J.C. Dickinson and Janez Povh:
    A new tractable approximation hierarchy for general polynomial optimization problems.
    (Preprint)

  3. Published in international peer reviewed journals

  4. Peter J.C. Dickinson:
    Erratum to: On the DJL conjecture for order 6.
    Operators and Matrices 11 (2017), Issue 4, 1197-1200.
    (Preprint)
  5. 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.
    (Preprint)
  6. Peter J.C. Dickinson and Roland Hildebrand:
    Considering Copositivity Locally.
    Journal of Mathematical Analysis and Applications 437 (2016), Issue 2, 1184-1195.
    (Preprint)
  7. 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.
    (Preprint)
  8. Peter J.C. Dickinson and Janez Povh:
    On an extension of Pólya's Positivstellensatz.
    Journal of Global Optimization. 61 (2015), Issue 4, 615-625.
    (Preprint)
    ✱ Recognised as one of the "Top-5 Papers Published in Journal of Global Optimization in 2015".
  9. 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.
    (Preprint)
  10. Peter J.C. Dickinson:
    On the Exhaustivity of Simplicial Partitioning.
    Journal of Global Optimization 58 (2014), Issue 1, 189-203.
    (Preprint)
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. Peter J.C. Dickinson:
    Geometry of the Copositive and Completely Positive Cones.
    Journal of Mathematical Analysis and Applications 380 (2011), Issue 1, 377-395.
  17. Peter J.C. Dickinson:
    An improved characterisation of the interior of the completely positive cone.
    Electronic Journal of Linear Algebra 20 (2010), 723-729.

  18. Miscellaneous publications

  19. 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).
  20. 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.

Excluding classes, I have so far given 40 presentations in 12 countries.
  1. 25.05.18: University Teaching Award presentation, University of Twente, The Netherlands:
    Friendship Paradox - Slides - Notes - Mathematica code
  2. 31.10.17: "Copositivity and Complete Positivity" workshop, Oberwolfach Research Institute for Mathematics, Germany:
    The structure of completely positive matrices according to their CP-rank and CP-plus-rank
  3. 20.07.17: IFORS, Quebec City, Canada:
    Considering Copositivity Locally
  4. 12.07.17: 15th EUROPT Workshop, Montréal, Canada:
    The structure of completely positive matrices according to their CP-rank and CP-plus-rank
  5. 20.07.16: MODU2016, Melbourne, Australia:
    Partitioning Simplices (see tweet from the talk)
  6. 12.01.16: Abacus Mathematisch Café, Twente, The Netherlands:
    Exhaustive Simplicial Partitioning
  7. 17.07.15: 22nd International Symposium on Mathematical Programming, Pittsburgh, U.S.A.:
    Scaling relationship between the copositive cone and Parrilo's first level approximation
  8. 09.07.15: 13th EUROPT Workshop, Edinburgh, Scotland:
    Considering Copositivity Locally
  9. 15.05.15: 3rd Alpen-Adria Workshop on Optimization 2015, Klagenfurt, Austria:
    Scaling relationship between the copositive cone and Parrilo's first level approximation
  10. 08.05.15: Mathematical Optimisation Symposium, Groningen, The Netherlands:
    Considering Copositivity Locally
  11. 19.03.15: Tenure Trackers bijeenkomst Wiskundeclusters - NWO, The Hague, The Netherlands:
    Copositive and Completely Positive Optimisation
  12. 09.01.15: 19th Combinatorial Optimization Workshop, Aussois, France:
    Considering the stability number of a graph via copositive optimisation
  13. 21.05.14: SIAM Conference on Optimization (OP14), San Diego, U.S.A.:
    A Nonlinear Semidefinite Approximation for Copositive Optimisation
  14. 23.10.13: Klagenfurt, Austria:
    An Application and Approximation for Copositive Optimisation
  15. 30.09.13: CWI, The Netherlands:
    Applications and Approximations for Copositive Optimisation
  16. 31.07.13: Polynomial Optimisation Programme, Cambridge, U.K.:
    On the set-copositive cone
  17. 24.07.13: ERGO Seminar, Edinburgh, U.K.:
    On a set-semidefinite representation of quadratic optimisation problems
  18. 17.07.13: Polynomial Optimisation Workshop, Cambridge, U.K.:
    A new convex reformulation and approximation hierarchy for polynomial optimisation
  19. 28.06.13: 11th EUROPT Workshop, Florence, Italy:
    On a set-semidefinite representation of quadratic optimisation problems
  20. 10.06.13: ISOR Colloquium, Vienna, Austria:
    Applications and Approximations for Copositive Optimisation
  21. 30.05.13 (Plenary speaker): DIAMANT symposium, Heeze, The Netherlands:
    Applications and Approximations for Copositive Optimisation
  22. 18.04.13: Operations Research Seminar, Tilburg, The Netherlands:
    Applications and Approximations for Copositive Optimisation
  23. 11.04.13: Mathematical Optimisation Symposium, Groningen, The Netherlands:
    Applications and Approximations for Copositive Optimisation
  24. 26.03.13: Industrial Engineering seminar, Twente, The Netherlands:
    Applications and Approximations for Copositive Optimisation
  25. 05.03.13: Combinatorics and Optimization seminar, CWI, Amsterdam, The Netherlands:
    Applications and Approximations for Set-semidefinite Optimisation
  26. 15.11.12: 2012 Haifa Matrix Theory conference, Haifa, Israel:
    The Interior of the completely positive cone
  27. 20.08.12: 21st International Symposium on Mathematical Programming, Berlin, Germany:
    Considering the complexity of complete positivity using the ellipsoid method
  28. 09.03.12: University of Iowa, U.S.A.:
    Copositive Programming
  29. 02.03.12: University of Waterloo, Canada:
    Checking if a Sparse Matrix is Completely Positive
  30. 01.03.12: University of Waterloo, Canada:
    Copositive Programming
  31. 02.11.11: SIAM Student Chapter, Trier, Germany:
    Copositive Programming
  32. 18.10.11: Novo Mesto, Slovenia:
    Copositive Programming
  33. 07.10.11: WONDER graduate student seminar Utrecht, The Netherlands:
    Copositive Programming
  34. 30.06.11: 3rd SDP day, CWI, Amsterdam, The Netherlands:
    Geometry of the Copositive and Completely Positive Cones
  35. 29.06.11: PhD Colloquium, Groningen, The Netherlands:
    An Improved Charactersation of the Interior of the Completely Positive Cone
  36. 17.05.11: SIAM Conference on Optimization, Darmstadt, Germany:
    Checking if a Sparse Matrix is Completely Positive
  37. 13.05.11: 2nd Alpen-Adria Workshop on Optimization 2011, Klagenfurt, Austria:
    Geometry of the Copositive and Completely Positive Cones
  38. 10.12.10: Intercity Number Theory Seminar, Groningen, The Netherlands:
    Linear-time checking of sparse matrices for complete positivity
  39. 09.09.10: 8th EUROPT Workshop, "Advances in Continuous Optimization", Aveiro, Portugal:
    An Improved Charactersation of the Interior of the Completely Positive Cone
  40. 14.04.10: Groningen Optimization Seminar, Groningen, The Netherlands:
    An Improved Charactersation of the Interior of the Completely Positive Cone