Convergence of a smoothing algorithm for symmetric cone complementarity problems with a nonmonotone line search |
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Authors: | ZhengHai Huang ShengLong Hu JiYe Han |
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Institution: | (1) Department of Mathematics, School of Science, Tianjin University, Tianjin, 300072, China;(2) Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China |
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Abstract: | In this paper, we propose a smoothing algorithm for solving the monotone symmetric cone complementarity problems (SCCP for
short) with a nonmonotone line search. We show that the nonmonotone algorithm is globally convergent under an assumption that
the solution set of the problem concerned is nonempty. Such an assumption is weaker than those given in most existing algorithms
for solving optimization problems over symmetric cones. We also prove that the solution obtained by the algorithm is a maximally
complementary solution to the monotone SCCP under some assumptions.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10571134, 10671010) and Natural Science
Foundation of Tianjin (Grant No. 07JCYBJC05200) |
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Keywords: | complementarity problem symmetric cone Euclidean Jordan algebra smoothing algorithm global convergence |
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