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Abstrakty
Two projection-type algorithms, different from the ones presented by Solodov & Tseng (1996) and He (1997) in the computation of stepsize, for solving pseudo-monotone variational inequality problems are presented. It is shown that the algorithms are globally convergent and, in addition, they are convergent R-linearly or Q-linearly under some mild conditions.
Czasopismo
Rocznik
Tom
Strony
157--165
Opis fizyczny
Bibliogr. 16 poz., wzory
Twórcy
autor
- Department of Applied Mathematics, Dalian University of Technology, 116024 Dalian, China
autor
- Department of Applied Mathematics, Dalian University of Technology, 116024 Dalian, China
Bibliografia
- [1] O. Arino: A note on the Discrete Lyapunov Function... Jornal of Differential Equations, 104(1), (1993), 169-181.
- [2] B. C. Eaves: On the basic theorem of complementarity. Math. Programming, 1 (1971), 68-75.
- [3] F. M. Gafni and D. P. Bertsekas: Two-metric projection methods for constrained optimizition. SIAM J. Control Optim., 22 (1984), 936-964.
- [4] P. T. Harker and J. S. Pang: Finite dimensional variational inequality and non-linear complementarity problems: a survey of theory, algorithms and applications. Math. Programming, 48 (1990). 161-220.
- [5] B. He: A class of projection and contraction methods for monotone variational inequalities. Appl. Math. Optim., 35 (1997), 69-76.
- [6] B. He: A projection and contraction method for a class of linear complementarity problems and its application in convex quadratic programming. Appl. Math. 25 (1992), 247-262.
- [7] B. He: A new method for a class of linear variational inequalities. Math. Programming, 66 (1994), 137-144.
- [8] S. Karamardian and S. Schaible: Seven kinds of monotone maps. J. Optim. Theorey and Appl., 66 (1990), 37-46.
- [9] Z. Luo, O. L. Mangasarian, J. Ren, and M. V. Solodov: New error bounds for the linear complementarity problem. Math. Open Res., 19 (1994), 880 892.
- [10] Z. Luo and J. S. Pang: Error bounds for analytic systems and their applications. Math. Programming, 67 (1994), 1-28.
- [11] Z. Luo and P. Tseng: Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem. SIAM J. Optim., 2 (1992), 43-54.
- [12] J. M. Ortega and W. C. Rheinboldt: Iterative solution of nonlinear equations in several variables. Academic Press, New York, 1970.
- [13] J. S. Pang and D. Chan: Iterative methods for variational inequality and complementarity problems. Math. Programming, 24 (1982), 284-313.
- [14] M. V. Solodov and P. Tseng: Modified projection-type methods for monotone variational inequalities. SIAM J. Control Optim., 34 (1996), 1814-1830.
- [15] D. Sun: A projection and contraction method for the nonlinear complementarity problem and its extensions. Math. Numer. Sinica, 16 (1994), 183-194.
- [16] P. Tseng: On linear convergence of iterative methods for the variational inequality problem. J. Comput. Appl Math., 60 (1995), 237-252.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BSW9-0011-2083