tailieunhanh - Báo cáo hóa học: " Research Article An Algorithm Based on Resolvant Operators for Solving Positively Semidefinite Variational Inequalities"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article An Algorithm Based on Resolvant Operators for Solving Positively Semidefinite Variational Inequalities | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 76040 15 pages doi 2007 76040 Research Article An Algorithm Based on Resolvant Operators for Solving Positively Semidefinite Variational Inequalities Juhe Sun Shaowu Zhang and Liwei Zhang Received 16 June 2007 Accepted 19 September 2007 Recommended by Nan-Jing Huang A new monotonicity M-monotonicity is introduced and the resolvant operator of an M-monotone operator is proved to be single-valued and Lipschitz continuous. With the help of the resolvant operator the positively semidefinite general variational inequality VI problem VI S F G is transformed into a fixed point problem of a nonexpan-sive mapping. And a proximal point algorithm is constructed to solve the fixed point problem which is proved to have a global convergence under the condition that F in the VI problem is strongly monotone and Lipschitz continuous. Furthermore a convergent path Newton method is given for calculating e-solutions to the sequence of fixed point problems enabling the proximal point algorithm to be implementable. Copyright 2007 Juhe Sun et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In recent years the variational inequality has been addressed in a large variety of problems arising in elasticity structural analysis economics transportation equilibrium optimization oceanography and engineering sciences 1 2 . Inspired by its wide applications many researchers have studied the classical variational inequality and generalized it in various directions. Also many computational methods for solving variational inequalities have been proposed see 3-8 and the references therein . Among these methods resolvant operator technique is an important one which was studied in the 1990s by many researchers such as 4 6 9 and