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Bio-Design and Manufacturing  2020 Vol.3 No.3 P.321~325

10.1631/jzus.2002.0321


A predictor-corrector interior-point algorithm for monotone variational inequality problems


Author(s):  LIANG Xi-ming, QIAN Ji-xin

Affiliation(s):  National Lab of Industrial Control Technology, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   x-into@mail.csut.edu.cn

Key Words:  Variational inequality problems (VIP), Predictor-corrector interior-point algorithm, Numerical experiments


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LIANG Xi-ming, QIAN Ji-xin. A predictor-corrector interior-point algorithm for monotone variational inequality problems[J]. Journal of Zhejiang University Science D, 2020, 3(3): 321~325.

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author="LIANG Xi-ming, QIAN Ji-xin",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0321"
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Abstract: 
Mehrotra's recent suggestion of a predictor-corrector variant of primal-dual interior-point method for linear programming is currently the interior-point method of choice for linear programming. In this work the authors give a predictor-corrector interior-point algorithm for monotone variational inequality problems. The algorithm was proved to be equivalent to a level-1 perturbed composite Newton method. Computations in the algorithm do not require the initial iteration to be feasible. Numerical results of experiments are presented.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

Reference

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[4] Liang, X. M., Xu, C. X., Hu, J. B., 2000. A potential reduction algorithm for monotone variational inequality problems. Systems Science and Mathematical Sciences, 13: 59-66.

[5] Mehrotra, S., 1990. On finding a vertex solution using interior-point methods. Linear Algebra Appl., 152: 233-253.

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[7] Sun, J., Zhao, G. Y., 1998. Quadratic convergence of a long-step interior-point method for nonlinear monotone variational inequality problems. J. Opti. Theo. Appl., 97: 471-491.

[8] Tseng, P., 1992. Global linear convergence of a path-following algorithm for some monotone variational inequality problems. J. Opti. Theo. Appl., 75: 265-279.

[9] Wu, J. H., 1993. A long-step primal path-following algorithm for some monotone variational inequality problems. Publication 959, Centre de Recherche sur les Transports, Université de Montréal.

[10] Wu, J. H., 1997. Modified primal path-following scheme for the monotone variational inequality problem. J. Opti. Theo. Appl., 95: 189-208.

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