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Extension of smoothing Newton algorithms to solve linear programming over symmetric cones

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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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Authors and Affiliations

  1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, China

    Zhenghai Huang & Xiaohong Liu

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  1. Zhenghai Huang
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  2. Xiaohong Liu
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Correspondence to Zhenghai Huang.

Additional information

This research is supported by the National Natural Science Foundation of China under Grant No. 10871144 and the Natural Science Foundation of Tianjin under Grant No. 07JCYBJC05200.

This paper was recommended for publication by Editor Shouyang WANG.

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Huang, Z., Liu, X. Extension of smoothing Newton algorithms to solve linear programming over symmetric cones. J Syst Sci Complex 24, 195–206 (2011). https://doi.org/10.1007/s11424-011-8045-0

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  • DOI: https://doi.org/10.1007/s11424-011-8045-0

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