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On proximal point-type algorithms for weakly convex functions and their connection to the backward Euler method

Tim Hoheisel(tim.hoheisel***at***mcgill.ca)
Maxime Laborde(maxime.laborde***at***mail.mcgill.ca)
Adam Oberman(adam.oberman***at***mcgill.ca)

Abstract: In this article we study the connection between proximal point methods for nonconvex optimization and the backward Euler method from numerical Ordinary Differential Equations (ODEs). We establish conditions for which these methods are equivalent. In the case of weakly convex functions, for small enough parameters, the implicit steps can be solved using a strongly convex objective function. In practice, this method can be faster than gradient descent. In this paper we find the optimal value of the regularization parameter.

Keywords: Proximal-point method, weak convexity, Moreau envelope, Euler method, $\theta$-method

Category 1: Convex and Nonsmooth Optimization

Citation:

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Entry Submitted: 05/04/2018
Entry Accepted: 05/04/2018
Entry Last Modified: 05/04/2018

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