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The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case

Author

Listed:
  • Stefania Bellavia

    (Università degli Studi di Firenze)

  • Gianmarco Gurioli

    (Institute of Information Science and Technologies “A. Faedo” ISTI-CNR)

  • Benedetta Morini

    (Università degli Studi di Firenze)

  • Philippe Louis Toint

    (University of Namur)

Abstract

Intrinsic noise in objective function and derivatives evaluations may cause premature termination of optimization algorithms. Evaluation complexity bounds taking this situation into account are presented in the framework of a deterministic trust-region method. The results show that the presence of intrinsic noise may dominate these bounds, in contrast with what is known for methods in which the inexactness in function and derivatives’ evaluations is fully controllable. Moreover, the new analysis provides estimates of the optimality level achievable, should noise cause early termination. Numerical experiments are reported that support the theory. The analysis finally sheds some light on the impact of inexact computer arithmetic on evaluation complexity.

Suggested Citation

  • Stefania Bellavia & Gianmarco Gurioli & Benedetta Morini & Philippe Louis Toint, 2023. "The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 700-729, February.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:2:d:10.1007_s10957-022-02153-5
    DOI: 10.1007/s10957-022-02153-5
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2013. "Gradient methods for minimizing composite functions," LIDAM Reprints CORE 2510, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. S. Gratton & Ph. L. Toint, 2020. "A note on solving nonlinear optimization problems in variable precision," Computational Optimization and Applications, Springer, vol. 76(3), pages 917-933, July.
    3. NESTEROV, Yurii, 2015. "Universal gradient methods for convex optimization problems," LIDAM Reprints CORE 2701, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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