Smoothing algorithms for complementarity problems over symmetric cones |
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Authors: | Zheng-Hai Huang Tie Ni |
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Institution: | 1.Department of Mathematics, School of Science,Tianjin University,Tianjin,People’s Republic of China |
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Abstract: | There recently has been much interest in studying optimization problems over symmetric cones. In this paper, we first investigate
a smoothing function in the context of symmetric cones and show that it is coercive under suitable assumptions. We then extend
two generic frameworks of smoothing algorithms to solve the complementarity problems over symmetric cones, and prove the proposed
algorithms are globally convergent under suitable assumptions. We also give a specific smoothing Newton algorithm which is
globally and locally quadratically convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic
tool which is extensively used in our analysis. Preliminary numerical results for second-order cone complementarity problems
are reported. |
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Keywords: | |
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