Comparison of Two Kinds of Prediction-Correction Methods for Monotone Variational Inequalities

Computational Optimization and Applications

Volumn 27, Issue 3, 2004, Pages 247-267

  He, Bingsheng ^a   Yuan, Xiaomino ^b   Zhang, Jason J Z ^b  

^a NANJING UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Extra gradient methods; Forward backward splitting methods; Monotone variational inequalities; Prediction correction methods

Indexed keywords

ALGORITHMS; FUNCTIONS; ITERATIVE METHODS; MAPPING; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING;

EXTRA-GRADIENT METHODS; FORWARD-BACKWARD SPLITTING METHODS; MONOTONE VARIATIONAL INEQUALITIES; PREDICTION-CORRECTION METHODS;

COMPUTATIONAL COMPLEXITY;

EID: 1342345850     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:COAP.0000013058.17185.90     Document Type: Article

References (28)

1. D.P. Bertsekas and J.N. Tsitsiklis, Parallel and Distributed Computation, Numerical Methods, Prentice-Hall: Englewood Cliffs, NJ, 1989.
2. R.W. Cottle, J.S. Pang, and R.E. Stone, The Linear Complementarity Problem: Academic Press: New York, 1992.
3. J. Douglas and H.H. Rachford, "On the numerical solution of the heat conduction problem in 2 and 3 space variables," Trans. Amer. Math. Soc., vol. 82, pp. 421-439, 1956.
4. B.C. Eaves, "On the basic theorem of complementarity," Mathematical Programming, vol. 1, pp. 68-75, 1971.
5. R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer-Verlag: New York, Berlin, Heidelberg, Tokyo, 1984.
6. A.A. Goldstein, "Convex programming in Hubert space," Bulletin of American Mathematical Society, vol. 70, pp. 709-710, 1964.
7. P.T. Harker and J.S. Pang, "Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory algorithms and applications," Mathematical Programming, vol. 48, pp. 161-220, 1990.
8. P.T. Harker and J.S. Pang, "A Damped-Newton method for the linear complementarity problem," Lectures in Applied Mathematics, vol. 26, pp. 265-284, 1990.
9. B.S. He, "A projection and contraction method for a class of linear complementarity problem and its application in convex quadratic programming," Applied Mathematics and Optimization, vol. 25, pp. 247-262, 1992.
10. B.S. He, "A new method for a class of linear variational inequalities," Mathematical Programming, vol. 66, pp. 137-144, 1994.
11. B.S. He, "Solving a class of linear projection equations," Numerische Mathematik, vol. 68, pp. 71-80, 1994.
12. B.S. He, "A class of projection and contraction methods for monotone variational inequalities," Applied Mathematics & Optimization, vol. 35, pp. 69-76, 1997.
13. B.S. He, "Inexact implicit methods for monotone general variational inequalities," Mathematical Programming, vol. 86, pp. 199-216, 1999.
14. B.S. He and L.Z. Liao, "Improvements of some projection methods for monotone nonlinear variational inequalities," J. of Optimization Theory and Applications, vol. 112, pp. 111-128, 2002.
15. E.N. Khobotov, "Modification of the extragradient method for solving variational inequalities and certain optimization problems," U.S.S.R. Comput. Math. Phys., vol. 27, pp. 120-127, 1987.
16. G.M. Korpelevich, "The extragradient method for finding saddle points and other problems," Ekonomika i Matematchskie Metody, vol. 12, pp. 747-756, 1976.
17. E.S. Levitin and B.T. Polyak, "Constrained minimization problems," USSR Computational Mathematics and Mathematical Physics, vol. 6, pp. 1-50, 1966.
18. P.L. Lions and B. Mercler, "Splitting algorithms for the sum of two nonlinear operators," SIAM J. Numerical Analysis, vol. 16, pp. 964-979, 1979.
19. P. Marcotte, "Application of Khobotov's algorithm to variational inequalities and network equilibrium problems," Inf. Syst. Oper. Res., vol. 29, pp. 258-270, 1984.
20. P. Marcotee and J.P. Dussault, "A note on a globally convergent newton method for solving variational inequalities," Operation Research Letters, vol. 6, pp. 35-42, 1987.
21. R.T. Rockafellar, "Augmented lagrangians and applications of the proximal point algorithm in convex programming," Mathematics of Operations Research, vol. 1, pp. 97-116, 1976.
22. M.V. Solodov and P. Tseng, "Modified projection-type methods for monotone variational inequalities," SIAM J. Control Optim, vol. 34, pp. 1814-1830, 1996.
23. D. Sun, "A projection and contraction method for the no-linear complementary problem and its extensions," Mathematica Numerica Sinica, vol. 16, pp. 183-194, 1994.
24. D. Sun, "A new stepsize skill for solving a class of nonlinear projection equations," Journal of Computational Mathematics, vol. 13, pp. 357-368, 1995.
25. D. Sun, "A class of iterative methods for solving nonlinear projection equations," Journal of Optimization Theory and Application, vol. 91, pp. 123-140, 1996.
26. K. Taji, M. Fukushima, and T. Ibaraki, "A globally convergent newton method for solving strongly monotone variational inequalities," Mathematical Programming, vol. 58, pp. 369-383, 1993.
27. P. Tseng, "A modified forward-backword splitting method for maximal monotone mappings," SIAM. J. Control. Optim., vol. 38, pp. 431-446, 2000.
28. G.L. Xue and Y.Y. Ye, "An efficient algorithm for minimizing a sum of Euclidean norms with applications," SIAM J. Optim., vol. 7, pp. 1017-1036, 1997.