Smooth Optimization with Approximate Gradient

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.

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Alexandre d'Aspremont
• Keywords: Optimal Complexity, SIAMJO 2008, Smooth First-order, Uniformly Bounded