Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: A unified approach

Guoyong Gu, Bingsheng He, Xiaoming YUAN*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models' structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way.

Original languageEnglish
Pages (from-to)135-161
Number of pages27
JournalComputational Optimization and Applications
Volume59
Issue number1-2
DOIs
Publication statusPublished - Oct 2014

Scopus Subject Areas

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Convergence rate
  • Convex minimization
  • Customized algorithms
  • Proximal point algorithm
  • Saddle-point problem
  • Splitting algorithms

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