期刊
MATHEMATICS OF OPERATIONS RESEARCH
卷 35, 期 3, 页码 641-654出版社
INFORMS
DOI: 10.1287/moor.1100.0456
关键词
coordinate descent; linear constraint; condition number; randomization; error bound; iterated projections; averaged projections; distance to ill-posedness; metric regularity
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 (Strohmer, T., R. Vershynin. 2009. A randomized Kaczmarz algorithm with exponential convergence. J. Fourier Anal. Appl. 15 262-278) 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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