Local convergence analysis of projection-type algorithms: unified approach
Journal of Optimization Theory and Applications
Some recent advances in projection-type methods for variational inequalities
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Convergence of a splitting inertial proximal method for monotone operators
Journal of Computational and Applied Mathematics
Splitting-type method for systems of variational inequalities
Computers and Operations Research
Variational Inequalities and Economic Equilibrium
Mathematics of Operations Research
Splitting-type method for systems of variational inequalities
Computers and Operations Research
Efficient Online and Batch Learning Using Forward Backward Splitting
The Journal of Machine Learning Research
Dual Averaging Methods for Regularized Stochastic Learning and Online Optimization
The Journal of Machine Learning Research
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Adaptive Fractional-order Multi-scale Method for Image Denoising
Journal of Mathematical Imaging and Vision
A splitting algorithm for dual monotone inclusions involving cocoercive operators
Advances in Computational Mathematics
| Hi-index | 0.00 |
Forward--backward splitting methods provide a range of approaches to solving large-scale optimization problems and variational inequalities in which structures conducive to decomposition can be utilized. Apart from special cases where the forward step is absent and a version of the proximal point algorithm comes out, efforts at evaluating the convergence potential of such methods have so far relied on Lipschitz properties and strong monotonicity, or inverse strong monotonicity, of the mapping involved in the forward step, the perspective mainly being that of projection algorithms. Here, convergence is analyzed by a technique that allows properties of the mapping in the backward step to be brought in as well. For the first time in such a general setting, global and local contraction rates are derived; moreover, they are derived in a form which makes it possible to determine the optimal step size relative to certain constants associated with the given problem. Insights are thereby gained into the effects of shifting strong monotonicity between the forward and backward mappings when a splitting is selected.