Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces

• Main Authors: Buong Nguyen, Kim JongKyu
• Format: Article
• Language: English
• Published: SpringerOpen 2010-01-01
• Series: Journal of Inequalities and Applications
• Online Access: http://www.journalofinequalitiesandapplications.com/content/2010/451916

<p/> <p>The purpose of this paper is to present a regularization variant of the inertial proximal point algorithm for finding a common element of the set of solutions for a variational inequality problem involving a hemicontinuous monotone mapping <inline-formula> <graphic file="1029-242X-2010-451916-i1.gif"/></inline-formula> and for a finite family of <inline-formula> <graphic file="1029-242X-2010-451916-i2.gif"/></inline-formula>-inverse strongly monotone mappings <inline-formula> <graphic file="1029-242X-2010-451916-i3.gif"/></inline-formula> from a closed convex subset <inline-formula> <graphic file="1029-242X-2010-451916-i4.gif"/></inline-formula> of a Hilbert space <inline-formula> <graphic file="1029-242X-2010-451916-i5.gif"/></inline-formula> into <inline-formula> <graphic file="1029-242X-2010-451916-i6.gif"/></inline-formula>.</p>