Improvements of some projection methods for monotone nonlinear variational inequalities

Journal of Optimization Theory and Applications

Volumn 112, Issue 1, 2002, Pages 111-128

  He, B S ^a   Liao, L Z ^b  

^a NANJING UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

explicit methods; implicit methods; Monotone variational inequalities; prediction correction methods

Indexed keywords

ELECTROMAGNETIC WAVE ATTENUATION; VARIATIONAL TECHNIQUES;

CORRECTION METHOD; EXPLICIT METHOD; IMPLICIT METHODS; MONOTONE VARIATIONAL INEQUALITY; PREDICTION-CORRECTION; PREDICTION-CORRECTION METHOD; PROJECTION METHOD; PROJECTION TYPES; TYPE METHODS; VARIATIONAL INEQUALITIES;

FORECASTING;

EID: 0036104161     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1013096613105     Document Type: Article

References (22)

1. GLOWINSKI, R., Numerical Methods for Nonlinear Variational Problems, Springer Verlag, New York, NY, 1984.
2. MARKER, P. T., and PANG, J. S., Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990.
3. XIAO, B., and HARKER, P. T., A Nonsmooth Newton Method for Variational Inequalities, I: Theory, Mathematical Programming, Vol. 65, pp. 151-194, 1994.
4. XIAO, B., and MARKER, P. T., A Nonsmooth Newton Method for Variational Inequalities, II: Numerical Results, Mathematical Programming, Vol. 65, pp. 195-216, 1994.
5. PANG, J. S., Inexact Newton Methods for the Nonlinear Complementarity Problem, Mathematical Programming, Vol. 36, pp. 54-71, 1986.
6. PANG, J. S., and QI, L., Nonsmooth Equations: Motivation and Algorithms, SIAM Journal on Optimization, Vol. 3, pp. 443-465, 1993.
7. MANGASARIAN, O. L., Solution of Symmetric Linear Complementarity Problems by Iterative Methods, Journal of Optimization Theory and Applications, Vol. 22, pp. 465-485, 1979.
8. HE, B. S., A Projection and Contraction Method for a Class of Linear Complementarity Problems and Its Application in Convex Quadratic Programming, Applied Mathematics and Optimization, Vol. 25, pp. 247-262, 1992.
9. HE, B. S., A New Method for a Class of Linear Variational Inequalities, Mathematical Programming, Vol. 66, pp. 137-144, 1994.
10. HE, B. S., Solving a Class of Linear Projection Equations, Numerische Mathematik, Vol. 68, pp. 71-80, 1994.
11. GOLDSTEIN, A. A., Convex Programming in Hilbert Space, Bulletin of the American Mathematical Society, Vol. 70, pp. 709-710, 1964.
12. LEVITIN, E. S., and POLYAK, B. T., Constrained Minimization Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 6, pp. 1-50, 1966.
13. BERTSEKAS, D. P., and GAFNI, E. M., Projection Methods for Variational Inequalities with Application to the Traffic Assignment Problem, Mathematical Programming Study, Vol. 17, pp. 139-159, 1982.
14. KORPELEVICH, G. M., The Extragradient Method for Finding Saddle Points and Other Problems, Ekonomika i Matematicheskie Metody, Vol. 12, pp. 747-756, 1976.
15. KHOBOTOV, E. N., Modification of the Extragradient Method for Solving Variational Inequalities and Certain Optimization Problems, USSR Computational Mathematics and Mathematical Physics, Vol. 27, pp. 120-127, 1987.
16. HE, B. S., A Class of Projection and Contraction Methods for Monotone Variational Inequalities, Applied Mathematics and Optimization, Vol. 35, pp. 69-76, 1997.
17. SUN, D. F., A Class of Iterative Methods for Solving Nonlinear Projection Equations, Journal of Optimization Theory and Applications, Vol. 91, pp. 123-140, 1996.
18. ROCKAFELLAR, R. T., Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming, Mathematics of Operations Research, Vol. 1, pp. 97-116, 1976.
19. BERTSEKAS, D. P., and TSITSIKLIS, J. N., Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1989.
20. HARKER, P. T., and PANG, J. S., A Damped Newton Method for the Linear Complementarity Problem, Lectures in Applied Mathematics Vol. 26, pp. 265-284, 1990.
21. MARCOTEE, P., and DUSSAULT, J. P., A Note on a Globally Convergent Newton Method for Solving Variational Inequalities, Operation Research Letters, Vol. 6, pp. 35-42, 1987.
22. TAJI, K., FUKUSHIMA, M., and IBARAKI, T., A Globally Convergent Newton Method for Solving Strongly Monotone Variational Inequalities, Mathematical Programming, Vol. 58, pp. 369-383, 1993.