SIAM Mathematics of Data Science (MDS20) Distinguished Lecture Series: Yurii Nesterov

/ May 19, 2020/

Inexact Accelerated High-order Proximal-point Methods

Abstract: In this talk, we present a new framework of Bi-Level Unconstrained Minimization (BLUM) for the development of accelerated methods in Convex Programming. These methods use approximations of the high-order proximal points, which are solutions of some auxiliary parametric optimization problems. For computing these points, we can use different methods, and, in particular, the lower-order schemes. This opens a possibility for the latter methods to overpass the traditional limits of the Complexity Theory. As an example, we obtain a new second-order method with the convergence rate O(k^(−4)), where k is the iteration counter. This rate is better than the maximal possible rate of convergence for this type of methods, as applied to functions with Lipschitz continuous Hessian. We also present new methods with the exact auxiliary search procedure, which have the rate of convergence O(k^(−(3p+1)/2)), where p≥1 is the order of the proximal operator. The auxiliary problem at each iteration of these schemes is convex.

Yurii Nesterov, Université Catholique de Louvain, Belgium

This is one of seven virtual plenary talks originally scheduled for the 2020 SIAM Conference on Mathematics of Data Science. For more information on this session, visit https://meetings.siam.org/sess/dsp_programsess.cfm?SESSIONCODE=69235. To view the virtual program and register for other invited plenary talks, minitutorial talks, and minisymposia, please visit the MDS20 website at https://www.siam.org/conferences/cm/conference/mds20