论文信息 - Three-step relaxed hybrid steepest-descent methods for variational inequalities

Three-step relaxed hybrid steepest-descent methods for variational inequalities

The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced.Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.

丁协平 | 林炎诚 | 姚任文

[1] Lu-Chuan Zeng,et al. On a General Projection Algorithm for Variational Inequalities , 1998 .

[2] D. Lamberton,et al. Variational inequalities and the pricing of American options , 1990 .

[3] L. Zeng. Completely Generalized Strongly Nonlinear Quasi-complementarity Problems in Hilbert Spaces , 1995 .

[4] R. Glowinski,et al. Numerical Methods for Nonlinear Variational Problems , 1985 .

[5] Lu-Chuan Zeng,et al. Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities , 2007 .

[6] Hong-Kun Xu,et al. Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities , 2003 .

[7] Hong-Kun Xu. Iterative Algorithms for Nonlinear Operators , 2002 .

[8] Lu-Chuan Zeng,et al. Iterative algorithm for finding approximate solutions to completely generalized strongly nonlinear quasivariational inequalities , 1996 .

[9] D. Kinderlehrer,et al. An introduction to variational inequalities and their applications , 1980 .

[10] I. Yamada. The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings , 2001 .

[11] W. A. Kirk,et al. Topics in Metric Fixed Point Theory , 1990 .

[12] Jen-Chih Yao,et al. Variational Inequalities with Generalized Monotone Operators , 1994, Math. Oper. Res..

[13] I. Konnov. Combined Relaxation Methods for Variational Inequalities , 2000 .