# Additive Schwarz Methods for Convex Optimization as Gradient Methods

@article{Park2020AdditiveSM, title={Additive Schwarz Methods for Convex Optimization as Gradient Methods}, author={Jongho Park}, journal={ArXiv}, year={2020}, volume={abs/1912.03617} }

This paper gives a unified convergence analysis of additive Schwarz methods for general convex optimization problems. Resembling the fact that additive Schwarz methods for linear problems are preco...

## 5 Citations

Preconditioning for finite element methods with strain smoothing

- Computer ScienceArXiv
- 2021

This work analyzes the spectrums of the stiffness matrices of the edge-based S-FEM and the SSE method and proposes an improved two-level additive Schwarz preconditioner for the strain smoothing methods by modifying local solvers appropriately.

Accelerated Additive Schwarz Methods for Convex Optimization with Adaptive Restart

- Computer ScienceJ. Sci. Comput.
- 2021

The proposed acceleration scheme for additive Schwarz methods does not require any a priori information on the levels of smoothness and sharpness of a target energy functional, so that it can be applied to various convex optimization problems.

Additive Schwarz Methods for Convex Optimization with Backtracking

- Computer ScienceComput. Math. Appl.
- 2022

Fast gradient methods for uniformly convex and weakly smooth problems

- Computer ScienceAdv. Comput. Math.
- 2022

Different from the existing works, fast gradient methods proposed in this paper do not use the restarting technique but use momentums that are suitably designed to reflect both the uniform convexity and weak smoothness information of the target energy function.

A dual‐primal finite element tearing and interconnecting method for nonlinear variational inequalities utilizing linear local problems

- MathematicsInternational Journal for Numerical Methods in Engineering
- 2021

We propose a novel dual‐primal finite element tearing and interconnecting method for nonlinear variational inequalities. The proposed method is based on a particular Fenchel–Rockafellar dual…

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