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Convergence Analysis of Perturbed Feasible Descent Methods

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  • M. V. Solodov

    (Instituto de Matemática Pura e Aplicada)

Abstract

We develop a general approach to convergence analysis of feasible descent methods in the presence of perturbations. The important novel feature of our analysis is that perturbations need not tend to zero in the limit. In that case, standard convergence analysis techniques are not applicable. Therefore, a new approach is needed. We show that, in the presence of perturbations, a certain ε-approximate solution can be obtained, where ε depends linearly on the level of perturbations. Applications to the gradient projection, proximal minimization, extragradient and incremental gradient algorithms are described.

Suggested Citation

  • M. V. Solodov, 1997. "Convergence Analysis of Perturbed Feasible Descent Methods," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 337-353, May.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:2:d:10.1023_a:1022602123316
    DOI: 10.1023/A:1022602123316
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    References listed on IDEAS

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    1. Jong-Shi Pang, 1987. "A Posteriori Error Bounds for the Linearly-Constrained Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 474-484, August.
    2. Z.-Q. Luo & O. L. Mangasarian & J. Ren & M. V. Solodov, 1994. "New Error Bounds for the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 880-892, November.
    3. O. L. Mangasarian, 1993. "Mathematical Programming in Neural Networks," INFORMS Journal on Computing, INFORMS, vol. 5(4), pages 349-360, November.
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    Cited by:

    1. M. V. Solodov & S. K. Zavriev, 1998. "Error Stability Properties of Generalized Gradient-Type Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 663-680, September.
    2. M. V. Solodov, 2003. "On Approximations with Finite Precision in Bundle Methods for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 151-165, October.
    3. Wenma Jin & Yair Censor & Ming Jiang, 2016. "Bounded perturbation resilience of projected scaled gradient methods," Computational Optimization and Applications, Springer, vol. 63(2), pages 365-392, March.

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