Smooth Optimization with Approximate Gradient

Details Smooth Optimization with Approximate Gradient Smooth Optimization with Approximate Gradient

2005-12-14

arxiv.org/abs/math/0512344v3

Mathematics

Optimization and Control

Titled changed from "Smooth Optimization for Sparse Semidefinite Programs". New figures, tests. Final version

Scientific paper

We show that the optimal complexity of Nesterov's smooth first-order optimization algorithm is preserved when the gradient is only computed up to a small, uniformly bounded error. In applications of this method to semidefinite programs, this means in some instances computing only a few leading eigenvalues of the current iterate instead of a full matrix exponential, which significantly reduces the method's computational cost. This also allows sparse problems to be solved efficiently using sparse maximum eigenvalue packages.

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