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Generalized proximal point algorithm for convex optimization

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Abstract

Ha (Ref. 1) recently introduced a generalized proximal point algorithm for solving a generalized equation. In this note, we present a generalized proximal point algorithm for convex optimization problems based on Ha's work. The idea behind this algorithm is that, instead of adding a quadratic term to all the variables, we add a quadratic term to a subset of the variables. We extend the criteria for approximate solutions given by Rockafellar (Ref. 2) and Auslender (Ref. 3) and present convergence results. Finally, we show how this algorithm can be applied to solve block-angular linear and quadratic programming problems.

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Authors and Affiliations

  1. Computer Science Telecommunications Program, University of Missouri-Kansas City, Kansas City, Missouri

    D. Medhi (Assistant Professor)

  2. ATT Bell Laboratories, Middletown, New Jersey

    C. D. Ha (Member of Technical Staff)

Authors
  1. D. Medhi
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  2. C. D. Ha
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Communicated by O. L. Mangasarian

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Medhi, D., Ha, C.D. Generalized proximal point algorithm for convex optimization. J Optim Theory Appl 88, 475–488 (1996). https://doi.org/10.1007/BF02192181

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  • DOI: https://doi.org/10.1007/BF02192181

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