New multiplier method for solving linear complementarity problems |
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Authors: | Ulji Guoqing Chen |
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Affiliation: | (1) Department of Mathematics, College of Science and Technology, Inner Mongolia University, Hohhot, 010021, China;(2) Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot, 010051, China |
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Abstract: | A new multiplier method for solving the linear complementarity problem LCP(q, M) is proposed. By introducing a Lagrangian of LCP(q, M), a new smooth merit function ϑ(x, λ) for LCP(q, M) is constructed. Based on it, a simple damped Newton-type algorithm with multiplier self-adjusting step is presented. When M is a P-matrix, the sequence {ϑ(x k, λ k)} (where {(x k, λ k)} is generated by the algorithm) is globally linearly convergent to zero and convergent in a finite number of iterations if the solution is degenerate. Numerical results suggest that the method is highly efficient and promising. Selected from Numerical Mathematics (A Journal of Chinese Universities), 2004, 26(2): 162–171 |
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Keywords: | linear complementarity problem multiplier method global linear convergence finite convergence |
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