Article ID: | iaor200971931 |
Country: | Germany |
Volume: | 70 |
Issue: | 2 |
Start Page Number: | 385 |
End Page Number: | 404 |
Publication Date: | Oct 2009 |
Journal: | Mathematical Methods of Operations Research |
Authors: | Liu Xiao-Hong, Huang Zheng-Hai |
Keywords: | cone decomposition |
In this paper, we introduce a one-parametric class of smoothing functions which contains the Fischer–Burmeister smoothing function and the Chen-Harker-Kanzow-Smale (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.