Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, April 03, 2012, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Sebastian Stich

The Heavy Ball Method

The classical gradient method is one of the main pillars of the successful story of modern convex optimization. Complexity analysis has revealed that the convergence rate of the gradient method is far from the theoretical lower bound. Although optimal methods have already been proposed in the 80s, they became popular not before the last decade.

We analyze the convergence rate of the gradient method on smooth strongly convex functions and present the lower complexity bound for this class. We introduce Polyak's Heavy Ball Method. This is one of the simplest multistep schemes which does not only have an easy physical explanation, but also achieves optimal convergence rate.

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