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On the inexact scaled gradient projection method

Author

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  • O. P. Ferreira

    (Universidade Federal de Goias)

  • M. Lemes

    (Universidade Federal de Goias)

  • L. F. Prudente

    (Universidade Federal de Goias)

Abstract

The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on the feasible set is computed, allowing for an appropriate relative error tolerance. Second, an inexact nonmonotone line search scheme is employed to compute a step size which defines the next iteration. It is shown that the proposed method has similar asymptotic convergence properties and iteration-complexity bounds as the usual scaled gradient projection method employing monotone line searches.

Suggested Citation

  • O. P. Ferreira & M. Lemes & L. F. Prudente, 2022. "On the inexact scaled gradient projection method," Computational Optimization and Applications, Springer, vol. 81(1), pages 91-125, January.
    • Handle: RePEc:spr:coopap:v:81:y:2022:i:1:d:10.1007_s10589-021-00331-1
    DOI: 10.1007/s10589-021-00331-1
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    References listed on IDEAS

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    1. Birgin, Ernesto G. & Martínez, Jose Mario & Raydan, Marcos, 2014. "Spectral Projected Gradient Methods: Review and Perspectives," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i03).
    2. Y. H. Dai, 2002. "On the Nonmonotone Line Search," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 315-330, February.
    3. Amir Beck & Marc Teboulle, 2004. "A conditional gradient method with linear rate of convergence for solving convex linear systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(2), pages 235-247, June.
    4. di Serafino, Daniela & Ruggiero, Valeria & Toraldo, Gerardo & Zanni, Luca, 2018. "On the steplength selection in gradient methods for unconstrained optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 176-195.
    5. Jun Fan & Liqun Wang & Ailing Yan, 2019. "An Inexact Projected Gradient Method for Sparsity-Constrained Quadratic Measurements Regression," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(02), pages 1-21, April.
    6. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    7. Geovani N. Grapiglia & Ekkehard W. Sachs, 2017. "On the worst-case evaluation complexity of non-monotone line search algorithms," Computational Optimization and Applications, Springer, vol. 68(3), pages 555-577, December.
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    Cited by:

    1. A. A. Aguiar & O. P. Ferreira & L. F. Prudente, 2023. "Inexact gradient projection method with relative error tolerance," Computational Optimization and Applications, Springer, vol. 84(2), pages 363-395, March.

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