A proximal gradient descent method for the extended second-order cone linear complementarity problem

Shaohua Pan, Jein Shan Chen*

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

8 引文 斯高帕斯(Scopus)

摘要

We consider an extended second-order cone linear complementarity problem (SOCLCP), including the generalized SOCLCP, the horizontal SOCLCP, the vertical SOCLCP, and the mixed SOCLCP as special cases. In this paper, we present some simple second-order cone constrained and unconstrained reformulation problems, and under mild conditions prove the equivalence between the stationary points of these optimization problems and the solutions of the extended SOCLCP. Particularly, we develop a proximal gradient descent method for solving the second-order cone constrained problems. This method is very simple and at each iteration makes only one Euclidean projection onto second-order cones. We establish global convergence and, under a local Lipschitzian error bound assumption, linear rate of convergence. Numerical comparisons are made with the limited-memory BFGS method for the unconstrained reformulations, which verify the effectiveness of the proposed method.

原文英語
頁(從 - 到)164-180
頁數17
期刊Journal of Mathematical Analysis and Applications
366
發行號1
DOIs
出版狀態已發佈 - 2010 6月 1

ASJC Scopus subject areas

  • 分析
  • 應用數學

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