Speaker: Professor Maicon Marques Alves

Department of Mathematics, Federal University of Santa Catarina in Florianópolis (Brazil)

Date:  November 17,  2021 at 10:00 am (Chilean-time)

Title:    Variants of the A-HPE and large-step A-HPE algorithms for strongly convex problems with applications to accelerated high-order tensor methods

Abstract:  For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove linear and the superlinear O(k^(-k(p-1)/(p+1))) global rates for the proposed variants of the A-HPE and large-step A-HPE methods, respectively. The parameter p >= 2  appears in the (high-order) large-step condition of the new large-step A-HPE algorithm. We apply our results to high-order tensor methods, obtaining a new inexact (relative-error) tensor method for (smooth) strongly convex optimization with iteration-complexity O(k^(-k(p-1)/(p+1))). In particular, for p=2, we obtain an inexact Newton-proximal algorithm with fast global O(k^(-k/3)) convergence rate.

Venue: Online via Google Meet: https://meet.google.com/xmu-cvfn-qkp

A brief biography of the speaker: M. Marques Alves is Associate Professor at the Department of Mathematics of the Federal University of Santa Catarina in Florianópolis (Brazil). He obtained his PhD in Mathematics from IMPA in 2009 and held a postdoctoral position at the Department of Industrial and Systems Engineering of the Georgia Institute of Technology (2014-2016). His current research interests include Algorithms for Convex Optimization, Monotone Operator Splitting Algorithms and applications to Statistical Learning and Inverse Problems.

Coordinators: Fabián Flores-Bazán (CMM, Universidad de Concepción) and Abderrahim Hantoute (Alicante)