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

Shaohua Pan, Jein Shan Chen

研究成果: 雜誌貢獻文章同行評審

5 引文 斯高帕斯(Scopus)

摘要

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.

原文英語
頁(從 - 到)3083-3100
頁數18
期刊Nonlinear Analysis, Theory, Methods and Applications
73
發行號9
DOIs
出版狀態已發佈 - 2010 十一月 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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