Speaker: Prof. Boris Mordukhovich

Distinguished University Professor of Mathematics Wayne State University

Date:  September 2, 2020 at 10:00

Title: Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization

Abstract: This talk aims at developing two versions of the generalized Newton method to compute local minimizers for nonsmooth problems of unconstrained and constraned optimization that satisfy an important stability property known as tilt stability. We start with unconstrained minimization of continuously differentiable cost functions having Lipschitzian gradients and suggest two second-order algorithms ofthe Newton type: one involving coderivatives of Lipschitzian gradient mappings, and the other based on graphical derivatives of the latter. Then we proceed with the propagation of these algorithms to minimization of extended-real-valued prox-regular functions, while covering in this way problems of constrained optimization, by using Moreau envelopes. Employing advanced techniques of second-order variational analysis and characterizations of tilt stability allows us to establish the solvability of subproblems in both algorithms and to prove the Q-superlinear convergence of their iterations. Based on joint work with Ebrahim Sarabi (Miami University, USA).

A recorded video of the conference is here;  the slides can be downloaded here

Venue: Online via Google Meet meet.google.com/gyf-mpcb-tre

A brief biography of the speaker: Prof. Boris Mordukhovich was born and educated in the former Soviet Union. He got his PhD from the Belarus State University (Minsk) in 1973. He is currently a Distinguished University Professor of Mathematics at Wayne State University. Mordukhovich is an expert in optimization, variational analysis, generalized differentiation, optimal control, and their applications to economics, engineering, behavioral sciences, and other fields. He is the author and a co-author of many papers and 5 monographs in these areas. Prof. Mordukhovich is an AMS Fellow, a SIAM Fellow, and a recipient of many international awards and honors including Doctor Honoris Causa degrees from 6 universities worldwide. He was the Founding Editor (2008) and a co-Editor-in-Chief (2009-2014) of Set-Valued and Variational Analysis, and is now an Associate Editor of many high-ranked journals including SIAM J. Optimization, JOTA, JOGO, etc. In 2016 he was elected to the Accademia Peloritana dei Pericolanti (Italy). Prof. Mordukhovich is in the list of Highly Cited Researchers in Mathematics.

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

Speaker: Prof. Emilio Vilches

Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

Date:  August 26, 2020 at 10:00

Title: An overview of Sweeping Processes with applications

Abstract: The Moreau’s Sweeping Process is a first-order differential inclusion, involving the normal cone to a moving set depending on time. It was introduced and deeply studied by J.J. Moreau in the 1970s as a model for an elastoplastic mechanical system. Since then, many other applications have been given, and new variants have appeared. In this talk, we review the latest developments in the theory of sweeping processes and its variants. We highlight open questions and provide some applications.

This work has been supported by ANID-Chile under project Fondecyt de Iniciación 11180098.

The recorded video of the conference can be downloaded here

The slides of the conference can be downloaded here

Venue: Online via Google Meet https://meet.google.com/toh-nxch-fhb

A brief biography of the speaker: Prof. Emilio Vilches is Assistant Professor at Universidad de O’Higgins, Rancagua, Chile. He obtains his Ph.D. from the University of Chile and the University of Burgundy in 2017. He is mainly interested in the application of convex and variational analysis to nonsmooth dynamical systems.

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

Speaker: Prof. Michel Théra
University of Limoges, France

Date: July 15, 2020 at 10:00

Abstract: The Moreau-Rockafellar subdifferential is a highly important notion in convex analysis and optimization theory. But there are many functions which fail to be subdifferentiable at certain points. In particular, there is a continuous convex function defined on $\ell^2(\mathbb{N})$, whose Moreau–Rockafellar subdifferential is empty at every point of its domain. This talk proposes some enlargements of the Moreau-Rockafellar subdifferential: the sup$^\star$-subdifferential, sup-subdifferential and symmetric subdifferential, all of them being nonempty for the mentioned function. These enlargements satisfy the most fundamental properties of the Moreau–Rockafellar subdifferential: convexity, weak$^*$-closedness, weak$^*$-compactness and, under some additional assumptions, possess certain calculus rules. The sup$^\star$ and sup subdifferentials coincide with the Moreau–Rockafellar subdifferential at every point at which the function attains its minimum, and if the function is upper semi-continuous, then there are some relationships for the other points. They can be used to detect minima and maxima of arbitrary functions.

The slides of the conference can be downloaded here.

Venue: Online via Google Meet – meet.google.com/unx-gcse-wkn

A brief biography of the speaker: Michel Théra is a French mathematician. He obtained his PhD from the Université de Pau et des Pays de l’Adour (1978) and his thèse d’Etat at the University of Panthéon-Sorbonne (1988). Former President of the French Society of Industrial and Applied Mathematics, he has been also Vice President of the University of Limoges in charge of the International Cooperation. He is presently a professor emeritus of Mathematics in the Laboratory XLIM from the University of Limoges, where he retired as Professeur de classe exceptionnelle. He became Adjoint Professor of Federation University Australia, chairing there the International Academic Advisory Group of the Centre for Informatics and Applied Optimisation (CIAO). He is also scientific co-director of the International School of Mathematics “Guido Stampacchia” at the“Ettore Majorana” Foundation and Centre for Scientific Culture (Erice, Sicily). During several years, he has been a member of the Committee for the Developing Countries of the European Mathematical Society and became after his term an associate member. His research focuses on variational analysis, convex analysis, continuous optimization, monotone operator theory and the interaction among these fields of research, and their applications. He has published 130 articles in international journals on various topics related to variational analysis, optimization, monotone operator theory and nonlinear functional analysis. He serves as editor for several journals on continuous optimization and has been responsible for several international research programs until his retirement.

Coordinators: Abderrahim Hantoute and Fabián Flores-Bazán (DIM-UdeC)

Speaker: Prof. Nicolas Hadjisavvas
University of the Aegean, Greece

Date: July 01, 2020 at 10:00

Abstract: Due to its definition through the epigraph, the usual asymptotic function of convex analysis is a very effective tool for studying minimization, especially of a convex function. However, it is not as convenient, if one wants to study maximization of a function “f”; this is done usually through the hypograph or, equivalently, through “−f”. We introduce a new concept of asymptotic function which allows us to simultaneously study convex and concave functions as well as quasi-convex and quasi-concave functions. We provide some calculus rules and relevant properties of the new asymptotic function for applications purposes. We also compare with the classical asymptotic function of convex analysis. By using the new concept of asymptotic function, we establish sufficient conditions for the non-emptiness and for the boundedness of the solution set of quasi-convex minimization problems and quasi-concave maximization problems.  Applications are given for quadratic and fractional quadratic problems.

This a joint work with F. Lara and D.T. Luc.

The slides of the conference can be downloaded here.

Venue: Online via Google Meet – https://meet.google.com/orv-dnim-cyq

A brief biography of the speaker: Prof. Nicolas Hadjisavvas  is Professor Emeritus at University of the Aegean, Greece. He is associate editor of JOTA, JOGO, Optimization, and Optim. Lett. He is author of 66 papers from which he received 1268 citations according to WoS (without self-citations). He edited 4 books in Springer, and 5 special journal issues. He has been the chair of the Working Group on Generalized Convexity (2003-2006, 2015-2018). He has been keynote or invited speaker in many Conferences or Summer Schools.

Coordinators: Abderrahim Hantoute and Fabián Flores-Bazán (DIM-UdeC)