CLC number: O242.2
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
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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 A, 2002, 3(3): 321-325.
@article{title="A predictor-corrector interior-point algorithm for monotone variational inequality problems",
author="LIANG Xi-ming, QIAN Ji-xin",
journal="Journal of Zhejiang University Science A",
volume="3",
number="3",
pages="321-325",
year="2002",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2002.0321"
}
%0 Journal Article
%T A predictor-corrector interior-point algorithm for monotone variational inequality problems
%A LIANG Xi-ming
%A QIAN Ji-xin
%J Journal of Zhejiang University SCIENCE A
%V 3
%N 3
%P 321-325
%@ 1869-1951
%D 2002
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2002.0321
TY - JOUR
T1 - A predictor-corrector interior-point algorithm for monotone variational inequality problems
A1 - LIANG Xi-ming
A1 - QIAN Ji-xin
J0 - Journal of Zhejiang University Science A
VL - 3
IS - 3
SP - 321
EP - 325
%@ 1869-1951
Y1 - 2002
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2002.0321
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.
[1] Auslender, A., Haddou, M., 1995. An interior-proximal method for convex linearly constrained problems and its extension to variational inequalities. Math. Prog., 71: 77-100.
[2] Harker, P. T., Pang, J. S., 1990. Finite-demensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and application. Math. Prog., 48: 161-220.
[3] Hock, W., Schittkowski, K., 1981. Test Examples for Nonlinear Programming Codes. Springer, Berlin. p.26-158.
[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.
[6] Ortega, M., Rheinboldt, W. C., 1970. Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York. p.97-168.
[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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