Abstract
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods for solving three closely related problems: a convex stochastic quadratic optimizati...
Highlights
In the era of big data where datasets become continuously larger, randomized iterative methods have become very popular, and they are playing a major role in areas like numerical linear algebra, scientific computing, and optimization
In the last part of the numerical evaluation we focus on randomized methods for solving the average consensus problem and describe how the proposed Inexact randomized block Kaczmarz (iRBK) can work as an efficient randomized gossip algorithm
In the last experiment we evaluate the performance of iRBK in both synthetic and real datasets
Summary
In the era of big data where datasets become continuously larger, randomized iterative methods have become very popular, and they are playing a major role in areas like numerical linear algebra, scientific computing, and optimization. They are preferred mainly because of their cheap per iteration cost which leads to the improvement in terms of complexity upon classical results by orders of magnitude and to the fact that they can scale to extreme dimensions. The purpose of this work is to reduce the cost of this step by incorporating inexact updates into the stochastic methods under study. In this paper we are interested in solving three closely related problems:
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