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Inexact gradient projection method with relative error tolerance

Author

Listed:
  • A. A. Aguiar

    (Universidade Federal de Goiás)

  • O. P. Ferreira

    (Universidade Federal de Goiás)

  • L. F. Prudente

    (Universidade Federal de Goiás)

Abstract

A gradient projection method with feasible inexact projections is proposed in the present paper. The inexact projection is performed using a general relative error tolerance. Asymptotic convergence analysis under quasiconvexity assumption and iteration-complexity bounds under convexity assumption of the method employing constant and Armijo step sizes are presented. Numerical results are reported illustrating the potential advantages of considering inexact projections instead of exact ones in some medium scale instances of a least squares problem over the spectrohedron.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:84:y:2023:i:2:d:10.1007_s10589-022-00425-4
    DOI: 10.1007/s10589-022-00425-4
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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