A homogeneous smoothing-type algorithm for symmetric cone linear programs |
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Authors: | Wei-Zhe Gu Zheng-Hai Huang |
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Institution: | 1. Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, China
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Abstract: | In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program ((SCLP) for short) by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of (SCLP). Furthermore, if (SCLP) has a solution, then the algorithm will generate a solution of (SCLP), and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of (SCLP). |
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Keywords: | linear program symmetric cone Euclidean Jordan algebra smoothing algorithm global conver-gence |
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