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Projective method of multipliers for linearly constrained convex minimization

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  • Majela Pentón Machado

    (UFBA, Universidade Federal da Bahia)

Abstract

We present a method for solving linearly constrained convex optimization problems, which is based on the application of known algorithms for finding zeros of the sum of two monotone operators (presented by Eckstein and Svaiter) to the dual problem. We establish convergence rates for the new method, and we present applications to TV denoising and compressed sensing problems.

Suggested Citation

  • Majela Pentón Machado, 2019. "Projective method of multipliers for linearly constrained convex minimization," Computational Optimization and Applications, Springer, vol. 73(1), pages 237-273, May.
    • Handle: RePEc:spr:coopap:v:73:y:2019:i:1:d:10.1007_s10589-019-00065-1
    DOI: 10.1007/s10589-019-00065-1
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    References listed on IDEAS

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    1. Jonathan Eckstein & Michael C. Ferris, 1998. "Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 218-235, May.
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    Cited by:

    1. Mauricio Romero Sicre, 2020. "On the complexity of a hybrid proximal extragradient projective method for solving monotone inclusion problems," Computational Optimization and Applications, Springer, vol. 76(3), pages 991-1019, July.
    2. Patrick R. Johnstone & Jonathan Eckstein, 2021. "Single-forward-step projective splitting: exploiting cocoercivity," Computational Optimization and Applications, Springer, vol. 78(1), pages 125-166, January.
    3. Majela Pentón Machado & Mauricio Romero Sicre, 2023. "A Projective Splitting Method for Monotone Inclusions: Iteration-Complexity and Application to Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 552-587, August.

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