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    A variable-penalty alternating directions method for convex optimization

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    A variable-penalty alternating directions method for convex optimization (300.3Kb)
    Date
    1995
    Author
    Kontogiorgis, Spyridon
    Meyer, Robert R.
    Metadata
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    Abstract
    We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which determine the new proximal terms and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration. This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems
    Subject
    block andular programs
    decomposition
    alternating direction methods
    parallel computing
    Permanent Link
    http://digital.library.wisc.edu/1793/65315
    Type
    Technical Report
    Citation
    95-18
    Part of
    • Math Prog Technical Reports

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