Comparison of Two Proximal Point Algorithms for Monotone Variational Inequalities

Since proximal point algorithms (abbreviated as PPA) are attractive for solving monotone variational inequality problems, various approximate versions of PPA (APPA) are developed for practical applications. In this paper, we make a comparison between two different versions of APPAs (APPA I and APPA II) in the literature which share some common properties. Both of the algorithms use the same inexactness restriction and the same step length. The only difference is that they use different search directions. Through theoretical analysis and numerical experiment, we can see that APPA II usually performs better than APPA I.