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math.OC2016
Gradient Descent Finds the Cubic-Regularized Non-Convex Newton Step
Yair Carmon, John C. Duchi
We consider the minimization of non-convex quadratic forms regularized by a cubic term, which exhibit multiple saddle points and poor local minima. Nonetheless, we prove that, unde…
math.OC2016★ 53 cited
Accelerated Methods for Non-Convex Optimization
Yair Carmon, John C. Duchi, Oliver Hinder +1
We present an accelerated gradient method for non-convex optimization problems with Lipschitz continuous first and second derivatives. The method requires time $O(ε^{-7/4} \log(1/…