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Decomposition via Alternating Linearization

Author

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  • K. Kiwiel
  • C.H. Rosa
  • A. Ruszczynski

Abstract

A new approximate proximal point method for minimizing the sum of two convex functions is introduced. It replaces the original problem by a sequence of regularized subproblems in which the functions are alternately represented by linear models. The method updates the linear models and the prox center, as well as the prox coefficient. It is monotone in terms of the objective values and converges to a solution of the problem, if any. A dual version of the method is derived and analyzed. Applications of the methods to multistage stochastic programming problems are discussed and preliminary numerical experience presented.

Suggested Citation

  • K. Kiwiel & C.H. Rosa & A. Ruszczynski, 1995. "Decomposition via Alternating Linearization," Working Papers wp95051, International Institute for Applied Systems Analysis.
    • Handle: RePEc:wop:iasawp:wp95051
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    File URL: http://www.iiasa.ac.at/Publications/Documents/WP-95-051.ps
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    References listed on IDEAS

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    1. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    2. Andrzej Ruszczyński, 1995. "On Convergence of an Augmented Lagrangian Decomposition Method for Sparse Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 634-656, August.
    3. A. Ruszczynski, 1994. "On Augmented Lagrangian Decomposition Methods For Multistage Stochastic Programs," Working Papers wp94005, International Institute for Applied Systems Analysis.
    4. A. Ruszczynski, 1992. "Augmented Lagrangian Decomposition for Sparse Convex Optimization," Working Papers wp92075, International Institute for Applied Systems Analysis.
    5. John M. Mulvey & Andrzej Ruszczyński, 1995. "A New Scenario Decomposition Method for Large-Scale Stochastic Optimization," Operations Research, INFORMS, vol. 43(3), pages 477-490, June.
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    Cited by:

    1. Necdet Aybat & Donald Goldfarb & Shiqian Ma, 2014. "Efficient algorithms for robust and stable principal component pursuit problems," Computational Optimization and Applications, Springer, vol. 58(1), pages 1-29, May.

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