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Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization


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  • Immanuel Bomze


  • Werner Schachinger
  • Gabriele Uchida
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    Bibliographic Info

    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 52 (2012)
    Issue (Month): 3 (March)
    Pages: 423-445

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    Handle: RePEc:spr:jglopt:v:52:y:2012:i:3:p:423-445

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    Keywords: Conic optimization; Copositive matrix; Completely positive matrix; Congruence; Hadamard product; Tensor product; Schur complement; Posynomial; Conic duality; Attainability; Feasibility; Copositive reformulation; Relaxation; Game theory; Friction and contact problem; Network stability; Reliability; Queueing; Traffic; Optimal control; Switched system; Robust optimization;


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    1. Berry, Michael W. & Browne, Murray & Langville, Amy N. & Pauca, V. Paul & Plemmons, Robert J., 2007. "Algorithms and applications for approximate nonnegative matrix factorization," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 155-173, September.
    2. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer, vol. 16(2), pages 111-125, June.
    3. A. Pinto da Costa & A. Seeger, 2010. "Cone-constrained eigenvalue problems: theory and algorithms," Computational Optimization and Applications, Springer, vol. 45(1), pages 25-57, January.
    4. Bomze, I.M. & Dür, M. & Klerk, E. de & Roos, C. & Quist, A.J. & Terlaky, T., 2000. "On copositive programming and standard quadratic optimization problems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-226128, Tilburg University.
    5. Quist, A.J. & Klerk, E. de & Roos, C. & Terlaky, T., 1998. "Copositive relaxation for general quadratic programming," Open Access publications from Tilburg University urn:nbn:nl:ui:12-226134, Tilburg University.
    6. Klerk, E. de, 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere: A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
    7. Richard Cottle, 2010. "A field guide to the matrix classes found in the literature of the linear complementarity problem," Journal of Global Optimization, Springer, vol. 46(4), pages 571-580, April.
    8. Klerk, E. de & Maharry, J. & Pasechnik, D.V. & Richter, B. & Salazar, G., 2006. "Improved bounds for the crossing numbers of Km,n and Kn," Open Access publications from Tilburg University urn:nbn:nl:ui:12-195047, Tilburg University.
    9. Dobre, C., 2011. "Semidefinite programming approaches for structured combinatorial optimization problems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4578463, Tilburg University.
    10. Klerk, E. de, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: A short survey," Open Access publications from Tilburg University urn:nbn:nl:ui:12-196764, Tilburg University.
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    Cited by:
    1. Peter Dickinson & Luuk Gijben, 2014. "On the computational complexity of membership problems for the completely positive cone and its dual," Computational Optimization and Applications, Springer, vol. 57(2), pages 403-415, March.
    2. Alexander Engau & Miguel Anjos & Immanuel Bomze, 2013. "Constraint selection in a build-up interior-point cutting-plane method for solving relaxations of the stable-set problem," Computational Statistics, Springer, vol. 78(1), pages 35-59, August.


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