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Abstract

Automated design of first-order optimization method

Adrien Taylor

Abstract:  In this talk, we will describe a novel constructive technique for
devising efficient first-order methods for a wide range of large-scale
convex minimization settings, including smooth, non-smooth, and strongly
convex minimization. The design technique takes an "ideal method",
performing a series of subspace-searches, and constructs a family of
methods sharing the same worst-case guarantees. We show that this
technique yields optimal methods in the smooth and non-smooth cases and
derive new methods for these cases, including methods that forego
knowledge of the problem parameters, at the cost of a one-dimensional
line search per iteration. In the strongly convex case, we show how
numerical tools can be used to perform the construction, and show that
resulting method offers an improved convergence rate compared to
Nesterov's celebrated fast gradient method.

This talk is mainly based on recent results obtained with Yoel Drori
(see https://arxiv.org/abs/1803.05676). The introductory part is based
on joint works with Julien Hendrickx, François Glineur, and Etienne de
Klerk.