On the convergence rate of Newton interior-point methods in the absence of strict complementarity |
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| Authors: | A. S. El-Bakry R. A. Tapia Y. Zhang |
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| Affiliation: | (1) Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt;(2) the Center for Research on Parallel Computations, Rice University, 77521-1892 Houston, Texas, USA;(3) Department of Computational and Applied Mathematics, Rice University, 77521-1892 Houston, Texas, USA;(4) the Center for Research on Parallel Computations, Rice University, 77521-1892 Houston, Texas, USA;(5) Department of Mathematics and Statistics, University of Maryland, Baltimore County, 21228 Baltimore, MD, USA |
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| Abstract: | In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1/4 for the Q1-factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the Q1 factor of the duality gap sequence is exactly 1/4. In addition, the convergence of the Tapia indicators is also discussed.This author was supported in part by NSF Coop. Agr. No. CCR-8809615 and AFOSR 89-0363 and the REDI Foundation.This author was supported in part by NSF Coop. Agr. No. CCR-8809615, AFOSR 89-0363, DOE DEFG05-86ER25017 and ARO 9DAAL03-90-G-0093.Visiting member of the Center for Research on Parallel Computations, Rice University, Houston, Texas, 77251-1892. This author was supported in part by DOE DE-FG02-93ER25171. |
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| Keywords: | interior-point methods linear convergence strict complementarity Q1-factors the Tapia indicators |
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