Study on Approximate Proximal Point Algorithms for Monotone Variational Inequalities

摘要

Proximal point algorithms (PPA) are attractive methods for solving monotone variational inequality problems. Since solving the sub-problem in each iteration exactly is costly or sometimes impossible, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, different versions of APPA in the literature are studied in parallel classes which share some common properties. The global convergence results for all discussed algorithms are proved under a uniform framework. The study clarifies the relationships and the related inexactness restrictions of various APPAs, hence provides a helpful guidance in choosing suitable APPAs in different application purposes. Finally, we report some numerical experiments of APPAs in applications.