Journal of Approximation Theory
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Journal of Computational and Applied Mathematics
Generalized Eckstein-Bertsekas proximal point algorithm based on A-maximal monotonicity design
Computers & Mathematics with Applications
A generalized proximal-point-based prediction-correction method for variational inequality problems
Journal of Computational and Applied Mathematics
Bregman functions and auxiliary problem principle
Optimization Methods & Software
Relaxed proximal point algorithms for variational inequalities with multi-valued operators
Optimization Methods & Software
Pseudomonotone$${_{\ast}}$$ maps and the cutting plane property
Journal of Global Optimization
Computers & Mathematics with Applications
Approximating zeros of monotone operators by proximal point algorithms
Journal of Global Optimization
Journal of Computational and Applied Mathematics
Pseudomonotone operators and the Bregman Proximal Point Algorithm
Journal of Global Optimization
Inexact Proximal Point Methods for Variational Inequality Problems
SIAM Journal on Optimization
On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean
SIAM Journal on Optimization
Generalized Eckstein-Bertsekas proximal point algorithm involving (H,η)-monotonicity framework
Mathematical and Computer Modelling: An International Journal
Mathematical and Computer Modelling: An International Journal
On the need for hybrid steps in hybrid proximal point methods
Operations Research Letters
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We present a new Bregman-function-based algorithm which is a modification of the generalized proximal point method for solving the variational inequality problem with a maximal monotone operator. The principal advantage of the presented algorithm is that it allows a more constructive error tolerance criterion in solving the proximal point subproblems. Furthermore, we eliminate the assumption of pseudomonotonicity which was, until now, standard in proving convergence for paramonotone operators. Thus we obtain a convergence result which is new even for exact generalized proximal point methods. Finally, we present some new results on the theory of Bregman functions. For example, we show that the standard assumption of convergence consistency is a consequence of the other properties of Bregman functions, and is therefore superfluous.