A Non-Interior Continuation Algorithm for the P0 or P* LCP with Strong Global and Local Convergence Properties |
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Authors: | Zheng-Hai Huang$ Jie Sun |
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Institution: | (1) Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, People's Republic of China;(2) Department of Decision Sciences, National University of Singapore, Singapore 119260, Republic of Singapore |
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Abstract: | We propose a non-interior continuation algorithm for the solution of the linear
complementarity problem (LCP) with a P0 matrix. The proposed algorithm
differentiates itself from the current continuation algorithms by combining good global
convergence properties with good local convergence properties under unified conditions.
Specifically, it is shown that the proposed algorithm is globally convergent under an
assumption which may be satisfied even if the solution set of the LCP is unbounded.
Moreover, the algorithm is globally linearly and locally superlinearly convergent under
a nonsingularity assumption. If the matrix in the LCP is a P* matrix, then the
above results can be strengthened to include global linear and local quadratic
convergence under a strict complementary condition without the nonsingularity
assumption. |
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Keywords: | Linear complementarity problem Non-interior continuation algorithm Global convergence Global linear convergence Local superlinear convergence |
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