An algorithm based on resolvant operators for solving positively semidefinite variational inequalities

Indexed by:期刊论文

Journal:FIXED POINT THEORY AND APPLICATIONS

Included Journals:SCIE

ISSN No.:1687-1820

Abstract: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(+)(n), F + G) is transformed into a fixed point problem of a nonexpansive 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 epsilon-solutions to the sequence of fixed point problems, enabling the proximal point algorithm to be implementable. Copyright (c) 2007.

Date of Publication:2007-01-01