کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
843160 908548 2008 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An algorithm based on resolvent operators for solving variational inequalities in Hilbert spaces
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
An algorithm based on resolvent operators for solving variational inequalities in Hilbert spaces
چکیده انگلیسی

In this paper, a new monotonicity, MM-monotonicity, is introduced, and the resolvent operator of an MM-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)(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 FF in the VI problem is strongly monotone and Lipschitz continuous. Furthermore, a convergent path Newton method, which is based on the assumption that the projection mapping ∏C(⋅)∏C(⋅) is semismooth, is given for calculating εε-solutions to the sequence of fixed point problems, enabling the proximal point algorithm to be implementable.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 69, Issue 10, 15 November 2008, Pages 3344–3357
نویسندگان
, , ,