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Convergence Analysis and Applications of the Glowinski–Le Tallec Splitting Method for Finding a Zero of the Sum of Two Maximal Monotone Operators

Author

Listed:
  • S. Haubruge

    (Universitaires, Notre Dame de la Paix)

  • V. H. Nguyen

    (Universitaires, Notre Dame de la Paix)

  • J. J. Strodiot

    (Universitaires, Notre Dame de la Paix)

Abstract

Many problems of convex programming can be reduced to finding a zero of the sum of two maximal monotone operators. For solving this problem, there exists a variety of methods such as the forward–backward method, the Peaceman–Rachford method, the Douglas–Rachford method, and more recently the θ-scheme. This last method has been presented without general convergence analysis by Glowinski and Le Tallec and seems to give good numerical results. The purpose of this paper is first to present convergence results and an estimation of the rate of convergence for this recent method, and then to apply it to variational inequalities and structured convex programming problems to get new parallel decomposition algorithms.

Suggested Citation

  • S. Haubruge & V. H. Nguyen & J. J. Strodiot, 1998. "Convergence Analysis and Applications of the Glowinski–Le Tallec Splitting Method for Finding a Zero of the Sum of Two Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 97(3), pages 645-673, June.
  • Handle: RePEc:spr:joptap:v:97:y:1998:i:3:d:10.1023_a:1022646327085
    DOI: 10.1023/A:1022646327085
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    References listed on IDEAS

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    1. Ciyou Zhu, 1995. "Asymptotic Convergence Analysis of the Forward-Backward Splitting Algorithm," Mathematics of Operations Research, INFORMS, vol. 20(2), pages 449-464, May.
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    Cited by:

    1. Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.
    2. Shi Zheng & Wen Zheng & Xia Jin, 2007. "Estimation of ARX parametric model in regional economic systems," Systems Engineering, John Wiley & Sons, vol. 10(4), pages 290-296, December.

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    1. Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.

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