Non-Interior Continuation Method for Solving the Monotone Semidefinite Complementarity Problem |
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Authors: | Huang and Han |
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Institution: | (1) Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, P.O. Box 2734, People's Republic of China, CN |
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Abstract: | Recently, Chen and Tseng extended non-interior continuation/ smooth- ing methods for solving linear/ nonlinear complementarity problems to semidefinite complementarity problems (SDCP). In this paper we propose a non-interior
continuation method for solving the monotone SDCP based on the smoothed Fischer—Burmeister function, which is shown to be
globally linearly and locally quadratically convergent under suitable assumptions. Our algorithm needs at most to solve a
linear system of equations at each iteration. In addition, in our analysis on global linear convergence of the algorithm,
we need not use the assumption that the Fréchet derivative of the function involved in the SDCP is Lipschitz continuous. For
non-interior continuation/ smoothing methods for solving the nonlinear complementarity problem, such an assumption has been used widely in the literature
in order to achieve global linear convergence results of the algorithms. |
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Keywords: | , Monotone semidefinite complementarity problem, Non-interior continuation method, Global linear convergence, Local,,,,,quadratic convergence, AMS Classification, 65K05, 90C25, 90C33, |
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