Entropic proximal mappings with applications to nonlinear programming
Mathematics of Operations Research
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
On the convergence of the exponential multiplier method for convex programming
Mathematical Programming: Series A and B
Entropy-like proximal methods in convex programming
Mathematics of Operations Research
Convergence rate analysis of nonquadratic proximal methods for convex and linear programming
Mathematics of Operations Research
Mathematical Programming: Series A and B
Proximal Minimization Methods with Generalized Bregman Functions
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B
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
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
Penalty/Barrier Multiplier Methods for Convex Programming Problems
SIAM Journal on Optimization
Rescaling and Stepsize Selection in Proximal Methods Using Separable Generalized Distances
SIAM Journal on Optimization
Interior projection-like methods for monotone variational inequalities
Mathematical Programming: Series A and B
Interior Gradient and Proximal Methods for Convex and Conic Optimization
SIAM Journal on Optimization
Double-Regularization Proximal Methods, with Complementarity Applications
Computational Optimization and Applications
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We present a new family of proximal point methods for solving monotone variational inequalities. Our algorithm has a relative error tolerance criterion in solving the proximal subproblems. Our convergence analysis covers a wide family of regularization functions, including double regularizations recently introduced by Silva, Eckstein, and Humes, Jr. [SIAM J. Optim., 12 (2001), pp. 238-261] and the Bregman distance induced by $h(x)=\sum_{i=1}^{n}x_{i}\log x_{i}$. We do not use in our analysis the assumption of paramonotonicity, which is standard in proving convergence of Bregman-based proximal methods.