On the Turing model complexity of interior point methods for semidefinite programming
July 13, 2015 Β· Declared Dead Β· π SIAM Journal on Optimization
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Authors
Etienne de Klerk, Frank Vallentin
arXiv ID
1507.03549
Category
math.OC: Optimization & Control
Cross-listed
cs.DS
Citations
38
Venue
SIAM Journal on Optimization
Last Checked
2 months ago
Abstract
It is known that one can solve semidefinite programs to within fixed accuracy in polynomial time using the ellipsoid method (under some assumptions). In this paper it is shown that the same holds true when one uses the short-step, primal interior point method. The main idea of the proof is to employ Diophantine approximation at each iteration to bound the intermediate bit-sizes of iterates.
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