A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones

作者：Liu Xiao Hong; Huang Zheng Hai^*

来源：Mathematical Methods of Operations Research, 2009, 70(2): 385-404.

DOI：10.1007/s00186-008-0274-1

• Linear programming
• Symmetric cone
• Euclidean Jordan algebra
• Smoothing Newton algorithm

In this paper, we introduce a one-parametric class of smoothing functions which contains the Fischer-Burmeister smoothing function and the CHKS smoothing function as special cases. Based on this class of smoothing functions, a smoothing Newton algorithm is extended to solve linear programming over symmetric cones. The global and local quadratic convergence results of the algorithm are established under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool in our analysis.

• 出版日期2009-10
• 单位天津大学