An Accelerated Dual Gradient Method and Applications in Viscoplasticity

Timm Treskatis, Miguel A. Moyers-Gonzalez, Chris J. Price

Published 2015-09-16Version 1

We present a very simple and fast algorithm for the numerical solution of a class of composite convex optimisation problems. Our FISTA-based accelerated dual gradient method (ADG) introduces no spurious regularisation, it relies on no heuristic parameters and it is ideally suited for large-scale problems. Furthermore, iterates converge to the exact solution at a rate of order $O(1/k)$, where $k$ is the iteration counter, compared to conventional first-order methods that only achieve $O(1/k^{0.5})$. In this paper, we derive these properties analytically and present numerical results for the application of stationary Bingham flow in two spatial dimensions. We demonstrate how the new algorithm ADG can be used to identify the free boundary between yielded and unyielded regions with previously unknown accuracy. Our results show that the new method outperforms the widespread alternating direction method of multipliers a.k.a. ALG2 by orders of magnitude.