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A framework of conjugate direction methods for symmetric linear systems in optimization

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  • Giovanni Fasano

    () (Dept. of Management, Università Ca' Foscari Venice)

Abstract

In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method, in order to preserve the conjugacy. For specific values of the parameters in our framework we obtain schemes equivalent to both the CG and the scaled-CG. We also prove the finite convergence of the algorithms in CD, and we provide some error analysis. Finally, preconditioning is introduced for CD, and we show that standard error bounds for the preconditioned CG also hold for the preconditioned CD.

Suggested Citation

  • Giovanni Fasano, 2013. "A framework of conjugate direction methods for symmetric linear systems in optimization," Working Papers 31, Department of Management, Università Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpdman:67
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    File URL: http://virgo.unive.it/wpideas/storage/2013wp31.pdf
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    1. Giovanni Fasano & Massimo Roma, 2013. "Preconditioning Newton–Krylov methods in nonconvex large scale optimization," Computational Optimization and Applications, Springer, vol. 56(2), pages 253-290, October.
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    Keywords

    Krylov-based Methods; Conjugate Direction Methods; Conjugacy Loss and Error Analysis; Preconditioning.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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