Randomized Methods for Linear Constraints: Convergence Rates and Conditioning

Details Randomized Methods for Linear Constraints: Convergence Rates and Conditioning Randomized Methods for Linear Constraints: Convergence Rates and Conditioning

2008-06-18

arxiv.org/abs/0806.3015v1

Mathematics

Optimization and Control

22 pages

Scientific paper

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of Strohmer and Vershynin for systems of linear equations, we show that, under appropriate probability distributions, the linear rates of convergence (in expectation) can be bounded in terms of natural linear-algebraic condition numbers for the problems. We relate these condition measures to distances to ill-posedness, and discuss generalizations to convex systems under metric regularity assumptions.

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