Smoothed Analysis of Renegar's Condition Number for Linear Programming (2002) [9 citations — 3 self]
Download:
http://research.microsoft.com/%7Ejdunagan/renegar.
http://research.microsoft.com/~jdunagan/smoothedan
CACHED:
|
http://research.microsoft.com/%7Ejdunagan/renegar.
http://research.microsoft.com/~jdunagan/smoothedan
CACHED:
|
by
John Dunagan
,
Daniel A. Spielman
,
Teng
,
Shang-hua Teng
In SIAM Conference on Optimization
Add To MetaCart
Popular Tags
No tags have been applied to this document.
BibTeX | Add To MetaCart
@INPROCEEDINGS{Dunagan02smoothedanalysis,
author = {John Dunagan and Daniel A. Spielman and Teng and Shang-hua Teng},
title = {Smoothed Analysis of Renegar's Condition Number for Linear Programming},
booktitle = {In SIAM Conference on Optimization},
year = {2002}
}
author = {John Dunagan and Daniel A. Spielman and Teng and Shang-hua Teng},
title = {Smoothed Analysis of Renegar's Condition Number for Linear Programming},
booktitle = {In SIAM Conference on Optimization},
year = {2002}
}
Bookmarks
OpenURL
Abstract:
For any linear program, we show that a slight random relative perturbation of that linear program has small condition number with high probability. Following [ST01], we call this smoothed analysis of the condition number. Part of our main result is that the expectation of the log of the condition number of any appropriately scaled linear program subject to a Gaussian perturbation of variance is at most O(log nd=) with high probability. Since the condition number bounds the running time of many algorithms for convex programming, this may explain their observed fast convergence. 1
