Abstract
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.
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This work was partially supported by the National Natural Science Foundation of China (Grants 10571134 and 10871144) and the Natural Science Foundation of Tianjin (Grant 07JCYBJC05200).
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Liu, XH., Huang, ZH. A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones. Math Meth Oper Res 70, 385–404 (2009). https://doi.org/10.1007/s00186-008-0274-1
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DOI: https://doi.org/10.1007/s00186-008-0274-1