An algorithm based on resolvent operators for solving variational inequalities in Hilbert spaces

作者：Sun Juhe^*; Zhang Liwei; Xiao Xiantao

来源：Nonlinear Analysis-Theory Methods & Applications, 2008, 69(10): 3344-3357.

DOI：10.1016/j.na.2007.09.026

• Hilbert space
• Cone
• M-Monotone operator
• Resolvent operator
• Variational inequality
• Convergence property

In this paper, a new monotonicity, M-monotonicity, is introduced, and the resolvent operator of an M-monotone operator is proved to be single valued and Lipschitz continuous. With the help of the resolvent operator, an equivalence between the variational inequality VI(C, F + G) and the fixed point problem of a nonexpansive mapping is established. 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, which is based on the assum

• 出版日期2008-11-15
• 单位大连理工大学