Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
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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.