Preconditioning via Diagonal Scaling
Optimization and Control
2016-10-14 v1
Abstract
Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient descent (SGD), the alternating direction method of multipliers (ADMM), and conjugate gradient (CG) in order to attain a modest accuracy in a reasonable number of iterations. In this report, we first discuss heuristics for diagonal scaling. Next, we motivate preconditioning by an example, and then we study preconditioning for a specific splitting form in ADMM called graph projection splitting. Finally we examine the performance of our methods by some numerical examples.
Cite
@article{arxiv.1610.03871,
title = {Preconditioning via Diagonal Scaling},
author = {Reza Takapoui and Hamid Javadi},
journal= {arXiv preprint arXiv:1610.03871},
year = {2016}
}