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A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs

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  • Enrico Bettiol

    (Université Paris 13, Sorbonne Paris Cité)

  • Lucas Létocart

    (Université Paris 13, Sorbonne Paris Cité)

  • Francesco Rinaldi

    (Università di Padova)

  • Emiliano Traversi

    (Université Paris 13, Sorbonne Paris Cité)

Abstract

Many real-world applications can usually be modeled as convex quadratic problems. In the present paper, we want to tackle a specific class of quadratic programs having a dense Hessian matrix and a structured feasible set. We hence carefully analyze a simplicial decomposition like algorithmic framework that handles those problems in an effective way. We introduce a new master solver, called Adaptive Conjugate Direction Method, and embed it in our framework. We also analyze the interaction of some techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments based on a benchmark of almost 1400 instances from specific and generic quadratic problems. We show the efficiency and robustness of the method when compared to a commercial solver (Cplex).

Suggested Citation

  • Enrico Bettiol & Lucas Létocart & Francesco Rinaldi & Emiliano Traversi, 2020. "A conjugate direction based simplicial decomposition framework for solving a specific class of dense convex quadratic programs," Computational Optimization and Applications, Springer, vol. 75(2), pages 321-360, March.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00151-4
    DOI: 10.1007/s10589-019-00151-4
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    References listed on IDEAS

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    1. Andrea Cristofari, 2019. "An almost cyclic 2-coordinate descent method for singly linearly constrained problems," Computational Optimization and Applications, Springer, vol. 73(2), pages 411-452, June.
    2. Gondzio, J. & du Merle, O. & Sarkissian, R. & Vial, J. -P., 1996. "ACCPM -- A library for convex optimization based on an analytic center cutting plane method," European Journal of Operational Research, Elsevier, vol. 94(1), pages 206-211, October.
    3. GOFFIN, Jean-Louis & VIAL, Jean-Philippe, 1990. "Cutting planes and column generation techniques with the projective algorithm," LIDAM Reprints CORE 918, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Christoph Buchheim & Emiliano Traversi, 2018. "Quadratic Combinatorial Optimization Using Separable Underestimators," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 424-437, August.
    5. Rostami, Borzou & Chassein, André & Hopf, Michael & Frey, Davide & Buchheim, Christoph & Malucelli, Federico & Goerigk, Marc, 2018. "The quadratic shortest path problem: complexity, approximability, and solution methods," European Journal of Operational Research, Elsevier, vol. 268(2), pages 473-485.
    6. Frank Curtis & Zheng Han & Daniel Robinson, 2015. "A globally convergent primal-dual active-set framework for large-scale convex quadratic optimization," Computational Optimization and Applications, Springer, vol. 60(2), pages 311-341, March.
    7. Syam, Siddhartha S., 1998. "A dual ascent method for the portfolio selection problem with multiple constraints and linked proposals," European Journal of Operational Research, Elsevier, vol. 108(1), pages 196-207, July.
    8. M. Santis & G. Pillo & S. Lucidi, 2012. "An active set feasible method for large-scale minimization problems with bound constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 395-423, October.
    9. Jacek Gondzio & Roy Kouwenberg, 2001. "High-Performance Computing for Asset-Liability Management," Operations Research, INFORMS, vol. 49(6), pages 879-891, December.
    10. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    11. Andrea Cristofari & Marianna Santis & Stefano Lucidi & Francesco Rinaldi, 2017. "A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 369-401, February.
    12. Gondzio, J. & Sarkissian, R. & Vial, J.-P., 1997. "Using an interior point method for the master problem in a decomposition approach," European Journal of Operational Research, Elsevier, vol. 101(3), pages 577-587, September.
    13. Gondzio, Jacek & González-Brevis, Pablo & Munari, Pedro, 2013. "New developments in the primal–dual column generation technique," European Journal of Operational Research, Elsevier, vol. 224(1), pages 41-51.
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