Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank
Optimization and Control
2020-12-22 v6
Abstract
In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first algorithm is based on the gradient descent in L1 norm instead of the Euclidean one. The second algorithm extends the Frank-Wolfe to support sparse gradient updates. The third algorithm stands for the mirror descent algorithm with a randomized projection. We proof converges rates for these methods for sparse problems as well as numerical experiments support their effectiveness.
Cite
@article{arxiv.1508.07607,
title = {Efficient Numerical Methods to Solve Sparse Linear Equations with Application to PageRank},
author = {Anton Anikin and Alexander Gasnikov and Alexander Gornov and Dmitry Kamzolov and Yury Maximov and Yurii Nesterov},
journal= {arXiv preprint arXiv:1508.07607},
year = {2020}
}
Comments
26 pages; Accepted to Optimization Methods and Software