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Planar Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization, Part 2: Application

Author

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  • G. Fasano

    (University of Rome-La Sapienza)

Abstract

In this paper, we describe an application of the planar conjugate gradient method introduced in Part 1 (Ref. 1) and aimed at solving indefinite nonsingular sets of linear equations. We prove that it can be used fruitfully within optimization frameworks; in particular, we present a globally convergent truncated Newton scheme, which uses the above planar method for solving the Newton equation. Finally, our approach is tested over several problems from the CUTE collection (Ref. 2).

Suggested Citation

  • G. Fasano, 2005. "Planar Conjugate Gradient Algorithm for Large-Scale Unconstrained Optimization, Part 2: Application," Journal of Optimization Theory and Applications, Springer, vol. 125(3), pages 543-558, June.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:3:d:10.1007_s10957-005-2088-0
    DOI: 10.1007/s10957-005-2088-0
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    Cited by:

    1. Andrea Caliciotti & Giovanni Fasano & Florian Potra & Massimo Roma, 2020. "Issues on the use of a modified Bunch and Kaufman decomposition for large scale Newton’s equation," Computational Optimization and Applications, Springer, vol. 77(3), pages 627-651, December.
    2. Renato De Leone & Giovanni Fasano & Yaroslav D. Sergeyev, 2018. "Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming," Computational Optimization and Applications, Springer, vol. 71(1), pages 73-93, September.
    3. Giovanni Fasano & Raffaele Pesenti, 2017. "Conjugate Direction Methods and Polarity for Quadratic Hypersurfaces," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 764-794, December.
    4. Renato Leone & Giovanni Fasano & Massimo Roma & Yaroslav D. Sergeyev, 2020. "Iterative Grossone-Based Computation of Negative Curvature Directions in Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 554-589, August.
    5. G. Fasano, 2007. "Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 267-285, February.
    6. Giovanni Fasano, 2015. "A Framework of Conjugate Direction Methods for Symmetric Linear Systems in Optimization," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 883-914, March.
    7. 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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