- On proximal point-type algorithms for weakly convex functions and their connection to the backward Euler method Tim Hoheisel(tim.hoheiselmcgill.ca) Maxime Laborde(maxime.labordemail.mcgill.ca) Adam Oberman(adam.obermanmcgill.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: Download: [PDF]Entry Submitted: 05/04/2018Entry Accepted: 05/04/2018Entry Last Modified: 05/04/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.