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Randomized Methods for Linear Constraints: Convergence Rates and Conditioning
Open accessAbstract
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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Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems
Nesterov, Y. (2012) · SIAM Journal on Optimization · doi:10.1137/100802001 · Cited by 1,187
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Bottou, L., Curtis, F. E., & Nocedal, J. (2018) · SIAM Review · doi:10.1137/16m1080173 · Cited by 3,128
Wright, S. J. (2015) · Mathematical Programming · doi:10.1007/s10107-015-0892-3 · Cited by 1,438
Efficiency of Coordinate Descent Methods on Huge-Scale Optimization Problems
Nesterov, Y. (2012) · SIAM Journal on Optimization · doi:10.1137/100802001 · Cited by 1,187
Richtárik, P., & Takáč, M. (2014) · Mathematical Programming · doi:10.1007/s10107-012-0614-z · Cited by 654
Randomized numerical linear algebra: Foundations and algorithms
Martinsson, P.-G., & Tropp, J. A. (2020) · Acta Numerica · doi:10.1017/s0962492920000021 · Cited by 300
Metadata
- Authors
- Leventhal, D., & Lewis, A. S.
- Venue
- Mathematics of Operations Research
- Published
- 2010-08
- Volume
- 35
- Issue
- 3
- Pages
- 641-654
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W2167820643
- Cited by
- 349
- References
- 2
- FWCI
- 7.77
- Type
- journal article
- Language
- en
- Open access
- green
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