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S. Mizuno, M. Todd, Y. Ye (1993)
On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear ProgrammingMath. Oper. Res., 18
Y. Ye, Osman Güler, R. Tapia, Yin Zhang (1993)
A quadratically convergent O( $$\sqrt n $$ L)-iteration algorithm for linear programmingMathematical Programming, 59
Z. Luo, Shi-Quan Wu (1994)
A modified predictor-corrector method for linear programmingComputational Optimization and Applications, 3
J. Ortega, W. Rheinboldt (2014)
Iterative solution of nonlinear equations in several variables
Z.Q. Luo, S.Q. Wu (1994)
A Modified Predictor-Corrector Method For LPComputational Optimization and Applications, 3
M. Kojima, N. Megiddo, Toshihito Noma, Akiko Yoshise (1991)
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R. Monteiro, I. Adler (1989)
Interior path following primal-dual algorithms. part I: Linear programmingMathematical Programming, 44
Y. Ye, K. Anstreicher (1993)
On quadratic and $$O\left( {\sqrt {nL} } \right)$$ convergence of a predictor—corrector algorithm for LCPMathematical Programming, 62
Recently, Ye et al. proved that the predictor-corrector method proposed by Mizuno et al. maintains $$O\left( {\sqrt n L} \right)$$ -iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a $$(\sqrt n \log ({1 \mathord{\left/ {\vphantom {1 \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }))$$ -iteration complexity while maintaining the quadratic asymptotic convergence.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 17, 2005
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