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Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints

Author

Listed:
  • S. Cafieri

    (Second University of Naples)

  • M. D’Apuzzo

    (Second University of Naples)

  • M. Marino

    (University of Naples Federico II)

  • A. Mucherino

    (Second University of Naples)

  • G. Toraldo

    (University of Naples Federico II)

Abstract

In this paper, we present an interior-point algorithm for large and sparse convex quadratic programming problems with bound constraints. The algorithm is based on the potential reduction method and the use of iterative techniques to solve the linear system arising at each iteration. The global convergence properties of the potential reduction method are reassessed in order to take into account the inexact solution of the inner system. We describe the iterative solver, based on the conjugate gradient method with a limited-memory incomplete Cholesky factorization as preconditioner. Furthermore, we discuss some adaptive strategies for the fill-in and accuracy requirements that we use in solving the linear systems in order to avoid unnecessary inner iterations when the iterates are far from the solution. Finally, we present the results of numerical experiments carried out to verify the effectiveness of the proposed strategies. We consider randomly generated sparse problems without a special structure. Also, we compare the proposed algorithm with the MOSEK solver.

Suggested Citation

  • S. Cafieri & M. D’Apuzzo & M. Marino & A. Mucherino & G. Toraldo, 2006. "Interior-Point Solver for Large-Scale Quadratic Programming Problems with Bound Constraints," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 55-75, April.
    • Handle: RePEc:spr:joptap:v:129:y:2006:i:1:d:10.1007_s10957-006-9043-6
    DOI: 10.1007/s10957-006-9043-6
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    References listed on IDEAS

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    1. Michael J. Todd & Yinyu Ye, 1990. "A Centered Projective Algorithm for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 508-529, August.
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    Cited by:

    1. Zhongyi Liu & Yue Chen & Wenyu Sun & Zhihui Wei, 2012. "A Predictor-corrector algorithm with multiple corrections for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 52(2), pages 373-391, June.
    2. S. Cafieri & M. D’Apuzzo & V. Simone & D. Serafino & G. Toraldo, 2007. "Convergence Analysis of an Inexact Potential Reduction Method for Convex Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 355-366, December.
    3. Cosmin Petra & Mihai Anitescu, 2012. "A preconditioning technique for Schur complement systems arising in stochastic optimization," Computational Optimization and Applications, Springer, vol. 52(2), pages 315-344, June.

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