Computational Optimization and Applications

, Volume 56, Issue 3, pp 559–572

A customized proximal point algorithm for convex minimization with linear constraints

Article

DOI: 10.1007/s10589-013-9564-5

Cite this article as:
He, B., Yuan, X. & Zhang, W. Comput Optim Appl (2013) 56: 559. doi:10.1007/s10589-013-9564-5

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.

Keywords

Convex minimizationProximal point algorithmResolvent operatorAugmented Lagrangian method

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.International Center of Management Science and Engineering and Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Department of MathematicsHong Kong Baptist UniversityHong KongChina
  3. 3.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduChina