Extension of smoothing Newton algorithms to solve linear programming over symmetric cones |
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Authors: | Zhenghai Huang Xiaohong Liu |
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Institution: | 1.Department of Mathematics, School of Science,Tianjin University,Tianjin,China |
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Abstract: | There recently has been much interest in studying some optimization problems over symmetric cones. This paper deals with linear
programming over symmetric cones (SCLP). The objective here is to extend the Qi-Sun-Zhou’s smoothing Newton algorithm to solve
SCLP, where characterization of symmetric cones using Jordan algebras forms the fundamental basis for our analysis. By using
the theory of Euclidean Jordan algebras, the authors show that the algorithm is globally and locally quadratically convergent
under suitable assumptions. The preliminary numerical results for solving the second-order cone programming are also reported. |
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