Interior proximal methods and central paths for convex second-order cone programming

Shaohua Pan, Jein-Shan Chen

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We make a unified analysis of interior proximal methods of solving convex second-order cone programming problems. These methods use a proximal distance with respect to second-order cones which can be produced with an appropriate closed proper univariate function in three ways. Under some mild conditions, the sequence generated is bounded with each limit point being a solution, and global rates of convergence estimates are obtained in terms of objective values. A class of regularized proximal distances is also constructed which can guarantee the global convergence of the sequence to an optimal solution. These results are illustrated with some examples. In addition, we also study the central paths associated with these distance-like functions, and for the linear SOCP we discuss their relations with the sequence generated by the interior proximal methods. From this, we obtain improved convergence results for the sequence for the interior proximal methods using a proximal distance continuous at the boundary of second-order cones.

Original languageEnglish
Pages (from-to)3083-3100
Number of pages18
JournalNonlinear Analysis, Theory, Methods and Applications
Volume73
Issue number9
DOIs
Publication statusPublished - 2010 Nov 1

Fingerprint

Convex Order
Interior Methods
Second-order Cone Programming
Proximal Methods
Central Path
Convex Programming
Convex Cone
Cones
Second-order Cone
Convergence Estimates
Limit Point
Global Convergence
Convergence Results
Univariate
Rate of Convergence
Optimal Solution
Closed

Keywords

  • Central path
  • Convergence
  • Convex second-order cone optimization
  • Interior proximal methods
  • Proximal distances with respect to SOCs

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Interior proximal methods and central paths for convex second-order cone programming. / Pan, Shaohua; Chen, Jein-Shan.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 73, No. 9, 01.11.2010, p. 3083-3100.

Research output: Contribution to journalArticle

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