# Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions

@inproceedings{TranDinh2021HalpernTypeAA, title={Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions}, author={Quoc Tran-Dinh and Yang Luo}, year={2021} }

In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov’s accelerating approach, our methods rely on a so-called Halpern-type fixed-point iteration in [32], and recently exploited by a number of researchers, including [24, 70]. Firstly, we derive a new variant of the anchored extra-gradient scheme in [70] based on Popov’s past extra-gradient method to solve a maximally monotone…

## 3 Citations

The Connection Between Nesterov's Accelerated Methods and Halpern Fixed-Point Iterations

- Mathematics
- 2022

We derive a direct connection between Nesterov’s accelerated first-order algorithm and the Halpern fixed-point iteration scheme for approximating a solution of a co-coercive equation. We show that…

A Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusion Problems

- Mathematics, Computer ScienceArXiv
- 2022

Stochastic monotone inclusion problems, which widely appear in machine learning applications, are studied, includ-ing robust regression and adversarial learning, and novel variants of stochastic Halpern iteration with recursive variance reduction are proposed.

Fast OGDA in continuous and discrete time

- Mathematics
- 2022

In the framework of real Hilbert spaces we study continuous in time dynamics as well as numerical algorithms for the problem of approaching the set of zeros of a single-valued monotone and continuous…

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