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An adaptive trust-region method without function evaluations

Author

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  • Geovani N. Grapiglia

    (Université catholique de Louvain, ICTEAM/INMA)

  • Gabriel F. D. Stella

    (Universidade Federal do Paraná)

Abstract

In this paper we propose an adaptive trust-region method for smooth unconstrained optimization. The update rule for the trust-region radius relies only on gradient evaluations. Assuming that the gradient of the objective function is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations required by the proposed method to generate approximate stationary points. As a corollary, we establish a global convergence result. We also present numerical results on benchmark problems. In terms of the number of calls of the oracle, the proposed method compares favorably with trust-region methods that use evaluations of the objective function.

Suggested Citation

  • Geovani N. Grapiglia & Gabriel F. D. Stella, 2022. "An adaptive trust-region method without function evaluations," Computational Optimization and Applications, Springer, vol. 82(1), pages 31-60, May.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:1:d:10.1007_s10589-022-00356-0
    DOI: 10.1007/s10589-022-00356-0
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    References listed on IDEAS

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    1. Geovani Nunes Grapiglia & Jinyun Yuan & Ya-xiang Yuan, 2016. "Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 980-997, December.
    2. Anna Heusinger & Christian Kanzow, 2009. "Optimization reformulations of the generalized Nash equilibrium problem using Nikaido-Isoda-type functions," Computational Optimization and Applications, Springer, vol. 43(3), pages 353-377, July.
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    Cited by:

    1. Geovani N. Grapiglia & Gabriel F. D. Stella, 2023. "An Adaptive Riemannian Gradient Method Without Function Evaluations," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1140-1160, June.

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