SIAM Journal on Control and Optimization
On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
A globally convergent Newton method for solving strongly monotone variational inequalities
Mathematical Programming: Series A and B
A proximal-based decomposition method for convex minimization problems
Mathematical Programming: Series A and B
Proximal Minimization Methods with Generalized Bregman Functions
SIAM Journal on Control and Optimization
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
A Logarithmic-Quadratic Proximal Method for Variational Inequalities
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels
Mathematics of Operations Research
Mathematics of Operations Research
A Relative Error Tolerance for a Family of Generalized Proximal Point Methods
Mathematics of Operations Research
Alternating Projection-Proximal Methods for Convex Programming and Variational Inequalities
SIAM Journal on Optimization
Convergence of Proximal-Like Algorithms
SIAM Journal on Optimization
A Generalized Proximal Point Algorithm for the Variational Inequality Problem in a Hilbert Space
SIAM Journal on Optimization
Journal of Optimization Theory and Applications
A New Hybrid Generalized Proximal Point Algorithm for Variational Inequality Problems
Journal of Global Optimization
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
A note on a globally convergent Newton method for solving monotone variational inequalities
Operations Research Letters
Computers & Mathematics with Applications
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In this paper, we propose a hybrid nonlinear decomposition-projection method for solving a class of monotone variational inequality problems. The algorithm utilizes the problems' structure conductive to decomposition and a projection step to get the next iterate. To make the method more practical, we allow solving of the subproblems approximately and adopt the constructive accuracy criterion developed recently by Solodov and Svaiter for classical proximal point algorithm and by the author for generalized proximal point algorithm. The Fejer monotonicity to the solution set of the problem is obtained by only assuming the underlying mapping is monotone and the solution set is nonempty. The parameter is allowed to vary in a larger interval than that of Auslender and Teboulle, and we also propose some improved self-adaptive strategies to choose the sequence of parameters, which makes the algorithm more flexible.