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Convergence of successive linear programming algorithms for noisy functions

Author

Listed:
  • Christoph Hansknecht

    (TU Braunschweig)

  • Christian Kirches

    (TU Braunschweig)

  • Paul Manns

    (TU Dortmund University)

Abstract

Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function and derivative information may be corrupted by noise, however. Sun and Nocedal have recently proposed a remedy for smooth unconstrained problems by means of a stabilization of the acceptance criterion for computed iterates, which leads to convergence of the iterates of a trust-region method to a region of criticality (Sun and Nocedal in Math Program 66:1–28, 2023. https://doi.org/10.1007/s10107-023-01941-9 ). We extend their analysis to the successive linear programming algorithm (Byrd et al. in Math Program 100(1):27–48, 2003. https://doi.org/10.1007/s10107-003-0485-4 , SIAM J Optim 16(2):471–489, 2005. https://doi.org/10.1137/S1052623403426532 ) for unconstrained optimization problems with objectives that can be characterized as the composition of a polyhedral function with a smooth function, where the latter and its gradient may be corrupted by noise. This gives the flexibility to cover, for example, (sub)problems arising in image reconstruction or constrained optimization algorithms. We provide computational examples that illustrate the findings and point to possible strategies for practical determination of the stabilization parameter that balances the size of the critical region with a relaxation of the acceptance criterion (or descent property) of the algorithm.

Suggested Citation

  • Christoph Hansknecht & Christian Kirches & Paul Manns, 2024. "Convergence of successive linear programming algorithms for noisy functions," Computational Optimization and Applications, Springer, vol. 88(2), pages 567-601, June.
    • Handle: RePEc:spr:coopap:v:88:y:2024:i:2:d:10.1007_s10589-024-00564-w
    DOI: 10.1007/s10589-024-00564-w
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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. Brian Irwin & Eldad Haber, 2023. "Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant condition," Computational Optimization and Applications, Springer, vol. 84(3), pages 651-702, April.
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