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It is known that one can solve semidefinite programs to within fixed accuracyin polynomial time using the ellipsoid method (under some assumptions). In thispaper it is shown that the same holds true when one uses the short-step, primalinterior point method. The main idea of the proof is to employ Diophantineapproximation at each iteration to bound the intermediate bit-sizes ofiterates.

On the Turing model complexity of interior point methods for semidefinite programming