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A customized proximal point algorithm for convex minimization with linear constraints

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Abstract

This paper demonstrates a customized application of the classical proximal point algorithm (PPA) to the convex minimization problem with linear constraints. We show that if the proximal parameter in metric form is chosen appropriately, the application of PPA could be effective to exploit the simplicity of the objective function. The resulting subproblems could be easier than those of the augmented Lagrangian method (ALM), a benchmark method for the model under our consideration. The efficiency of the customized application of PPA is demonstrated by some image processing problems.

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Authors and Affiliations

  1. International Center of Management Science and Engineering and Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Bingsheng He

  2. Department of Mathematics, Hong Kong Baptist University, Hong Kong, China

    Xiaoming Yuan

  3. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Wenxing Zhang

Authors
  1. Bingsheng He
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  2. Xiaoming Yuan
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  3. Wenxing Zhang
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Corresponding author

Correspondence to Xiaoming Yuan.

Additional information

B. He was supported by the NSFC grant 91130007 and the grant of MOE of China 20110091110004.

X. Yuan was supported by the General Research Fund from Hong Kong Research Grants Council: 203712.

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He, B., Yuan, X. & Zhang, W. A customized proximal point algorithm for convex minimization with linear constraints. Comput Optim Appl 56, 559–572 (2013). https://doi.org/10.1007/s10589-013-9564-5

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