Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
Matrix computations (3rd ed.)
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
Improvements of some projection methods for monotone nonlinear variational inequalities
Journal of Optimization Theory and Applications
Comparison of Two Kinds of Prediction-Correction Methods for Monotone Variational Inequalities
Computational Optimization and Applications
Computational Optimization and Applications
Computational Optimization and Applications
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Approximate proximal point algorithms (abbreviated as APPAs) are classical approaches for convex optimization problems and monotone variational inequalities. In Part I of this paper (He et al. in Proximal-like contraction methods for monotone variational inequalities in a unified framework I: effective quadruplet and primary methods, 2010), we proposed a unified framework consisting of an effective quadruplet and a corresponding accepting rule. Under the framework, various existing APPAs can be grouped in the same class of methods (called primary or elementary methods) which adopt one of the geminate directions in the effective quadruplet and take the unit step size. In this paper, we extend the primary methods by using the same effective quadruplet and the accepting rule. The extended (general) contraction methods need only minor extra even negligible costs in each iteration, whereas having better properties than the primary methods in sense of the distance to the solution set. A set of matrix approximation examples as well as six other groups of numerical experiments are constructed to compare the performance between the primary (elementary) and extended (general) methods. As expected, the numerical results show the efficiency of the extended (general) methods are much better than that of the primary (elementary) ones.