Stochastic Forward–Backward Splitting for Monotone Inclusions
@article{Rosasco2016StochasticFS, title={Stochastic Forward–Backward Splitting for Monotone Inclusions}, author={Lorenzo Rosasco and Silvia Villa and Bang C{\^o}ng Vu}, journal={Journal of Optimization Theory and Applications}, year={2016}, volume={169}, pages={388-406} }
We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward–backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as well as almost sure convergence under weaker assumptions. For minimization problems, we recover rates matching those obtained…
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References
SHOWING 1-10 OF 68 REFERENCES
Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators
- Mathematics
- 2015
We investigate the asymptotic behavior of a stochastic version of the forward-backward splitting algorithm for finding a zero of the sum of a maximally monotone set-valued operator and a cocoercive…
A stochastic inertial forward–backward splitting algorithm for multivariate monotone inclusions
- Mathematics, Computer Science
- 2015
Almost sure convergence in real Hilbert spaces of the sequence of iterates to an optimal solution is established and two new classes of stochastic inertial primal–dual splitting methods for solving structured systems of composite monotone inclusions are introduced.
Solving monotone inclusions via compositions of nonexpansive averaged operators
- Mathematics
- 2004
A unified fixed point theoretic framework is proposed to investigate the asymptotic behavior of algorithms for finding solutions to monotone inclusion problems. The basic iterative scheme under…
Solving variational inequalities with Stochastic Mirror-Prox algorithm
- Mathematics, Computer Science
- 2008
A novel Stochastic Mirror-Prox algorithm is developed for solving s.v.i. variational inequalities with monotone operators and it is shown that with the convenient stepsize strategy it attains the optimal rates of convergence with respect to the problem parameters.
Accelerated and Inexact Forward-Backward Algorithms
- Computer ScienceSIAM J. Optim.
- 2013
We propose a convergence analysis of accelerated forward-backward splitting methods for composite function minimization, when the proximity operator is not available in closed form, and can only be…
Regularized Iterative Stochastic Approximation Methods for Stochastic Variational Inequality Problems
- MathematicsIEEE Transactions on Automatic Control
- 2013
This work introduces two classes of stochastic approximation methods, each of which requires exactly one projection step at every iteration, and provides convergence analysis for each of them.
On the maximal monotonicity of subdifferential mappings.
- Mathematics
- 1970
The subdifferential of a lower semicontinuous proper convex function on a Banach space is a maximal monotone operator, as well as a maximal cyclically monotone operator. This result was announced by…
Stochastic quasi-Fejér block-coordinate fixed point iterations with random sweeping II: mean-square and linear convergence
- Mathematics, Computer ScienceSIAM J. Optim.
- 2015
Results on the mean-square and linear convergence of the iterates of the block-coordinate fixed point algorithms are established and applications to monotone operator splitting and proximal optimization algorithms are presented.