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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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  • Immanuel Bomze & Werner Schachinger & Gabriele Uchida, 2012. "Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 423-445, March.
    • Handle: RePEc:spr:jglopt:v:52:y:2012:i:3:p:423-445
    DOI: 10.1007/s10898-011-9749-3
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    References listed on IDEAS

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    1. de Klerk, E. & Laurent, M. & Parrilo, P., 2005. "On the equivalence of algebraic approaches to the minimization of forms on the simplex," Other publications TiSEM 894d686e-2a57-43b2-b03a-a, Tilburg University, School of Economics and Management.
    2. 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.
    3. Mohan, S.R. & Talman, A.J.J., 1998. "Refinement of solutions to the linear complimentarity problem," Discussion Paper 1998-78, Tilburg University, Center for Economic Research.
    4. T. E. S. Raghavan & Zamir Syed, 2002. "Computing Stationary Nash Equilibria of Undiscounted Single-Controller Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 384-400, May.
    5. Karthik Natarajan & Chung Piaw Teo & Zhichao Zheng, 2011. "Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation," Operations Research, INFORMS, vol. 59(3), pages 713-728, June.
    6. C. Humes & J. Ou & P. R. Kumar, 1997. "The Delay of Open Markovian Queueing Networks: Uniform Functional Bounds, Heavy Traffic Pole Multiplicities, and Stability," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 921-954, November.
    7. Masakazu Kojima & Nimrod Megiddo & Shinji Mizuno, 1993. "A General Framework of Continuation Methods for Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 945-963, November.
    8. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    9. 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.
    10. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
    11. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    12. A. Hassouni & A. Lahlou & A. Lamghari, 2005. "Existence Theorems for Linear Complementarity Problems on Solid Closed Convex Cones," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 225-246, August.
    13. M. V. Solodov, 1997. "Stationary Points of Bound Constrained Minimization Reformulations of Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 449-467, August.
    14. de Klerk, E., 2008. "The complexity of optimizing over a simplex, hypercube or sphere : A short survey," Other publications TiSEM 485b6860-cf1d-4cad-97b8-2, Tilburg University, School of Economics and Management.
    15. Dobre, C., 2011. "Semidefinite programming approaches for structured combinatorial optimization problems," Other publications TiSEM e1ec09bd-b024-4dec-acad-7, Tilburg University, School of Economics and Management.
    16. 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.
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    Citations

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    Cited by:

    1. João Gouveia & Ting Kei Pong & Mina Saee, 2020. "Inner approximating the completely positive cone via the cone of scaled diagonally dominant matrices," Journal of Global Optimization, Springer, vol. 76(2), pages 383-405, February.
    2. Andrey Afonin & Roland Hildebrand & Peter J. C. Dickinson, 2021. "The extreme rays of the $$6\times 6$$ 6 × 6 copositive cone," Journal of Global Optimization, Springer, vol. 79(1), pages 153-190, January.
    3. Abdeljelil Baccari & Mourad Naffouti, 2016. "Copositivity and Sparsity Relations Using Spectral Properties," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 998-1007, December.
    4. Bomze, Immanuel M. & Gabl, Markus, 2023. "Optimization under uncertainty and risk: Quadratic and copositive approaches," European Journal of Operational Research, Elsevier, vol. 310(2), pages 449-476.
    5. 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," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 35-59, August.
    6. Zhijian Lai & Akiko Yoshise, 2022. "Completely positive factorization by a Riemannian smoothing method," Computational Optimization and Applications, Springer, vol. 83(3), pages 933-966, December.
    7. 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.
    8. Immanuel M. Bomze & Jianqiang Cheng & Peter J. C. Dickinson & Abdel Lisser & Jia Liu, 2019. "Notoriously hard (mixed-)binary QPs: empirical evidence on new completely positive approaches," Computational Management Science, Springer, vol. 16(4), pages 593-619, October.
    9. Carmo Brás & Gabriele Eichfelder & Joaquim Júdice, 2016. "Copositivity tests based on the linear complementarity problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 461-493, March.
    10. Faizan Ahmed & Mirjam Dür & Georg Still, 2013. "Copositive Programming via Semi-Infinite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 322-340, November.
    11. Immanuel M. Bomze & Bo Peng, 2023. "Conic formulation of QPCCs applied to truly sparse QPs," Computational Optimization and Applications, Springer, vol. 84(3), pages 703-735, April.

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