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arXiv · 1610.03871

Preconditioning via Diagonal Scaling

Reza Takapoui·Hamid Javadi
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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.

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Reza Takapoui, Hamid Javadi. 2016-10-12. Preconditioning via Diagonal Scaling. https://arxiv.org/abs/1610.03871

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