Optimization Seminars
Center for Mathematical Modeling – U. de Chile
On the construction of maximal p-cyclically monotone operators
14 de January de 2021 Seminarfflores
Speaker: Professor Orestes Bueno
Universidad del Pacífico, Lima, Perú
Date: January 20, 2021 at 10:00 (Chilean-time)
Title: On the construction of maximal p-cyclically monotone operators
Abstract: In this talk we deal with the construction of explicit examples of maximal p-cyclically maximal monotone operators. To the date, there is only one instance of an explicit example of a maximal 2-cyclically monotone operator that is not maximal monotone. We present several other examples, and a proposal of how such examples can be constructed.
A recorded video of the conference is …. ; the slides can be downloaded here
Venue: Online via Google Meet http://meet.google.com/mqh-bgjv-iyb
A brief biography of the speaker: Orestes Bueno is an Associate Professor at Universidad del Pacífico, Lima, Perú. He obtained his PhD at the Instituto de Matemática Pura e Aplicada (IMPA), Brazil, in 2012. His main interests are: Maximal Monotone Operators, Generalized Convexity and Monotonicity, Functional Analysis.
Coordinators: Fabián Flores-Bazán (Universidad de Concepción) and Abderrahim Hantoute (CMM).
On diametrically maximal sets, maximal premonotone maps and premonotone bifunctions
13 de November de 2020 Seminarfflores
Speaker: Professor Wilfredo Sosa
Graduate Program of Economics, Catholic University of Brasilia, Brazil
Date: November 18, 2020 at 10:00
Title: On diametrically maximal sets, maximal premonotone maps and premonotone bifunctions
Abstract: First, we study diametrically maximal sets in the Euclidean space (those which are not properly contained in a set with the same diameter), establishing their main properties. Then, we use these sets for exhibiting an explicit family of maximal premonotone operators. We also establish some relevant properties of maximal premonotone operators, like their local boundedness, and finally we introduce the notion of premonotone bifunctions, presenting a canonical relation between premonotone operators and bifunctions, that extends the well known one, which holds in the monotone case.
Venue: Online via Google Meet meet.google.com/tam-ddhj-psx
A brief biography of the speaker: Wilfredo Sosa es profesor del Programa de Graduados de Economía de la Universidad Católica de Brasilia, Brazil; Egresado de la Universidad de Ingeniería de Lima, Perú. Formado en el IMPA de Rio de Janeiro Brasil. Co-Fundador del IMCA de Lima Peru. Miembro titular de la Academia de Ciencias de Perú. Areas de interés: Optimization theory; Duality theory; Equilibrium theory; Mathematical economy.
Coordinators: Fabián Flores-Bazán (Universidad de Concepción) and Abderrahim Hantoute (CMM)
An algebraic view of the smallest strictly monotonic function
31 de October de 2020 Seminarfflores
Speaker: Professor César Gutiérrez
IMUVA (Mathematics Research Institute of the University of Valladolid), Valladolid, Spain
Title: An algebraic view of the smallest strictly monotonic function
Abstract: The talk concerns with one of the most popular functions to derive nonconvex separation results. Complete characterizations for both its level sets and basic properties such as monotonicity and convexity are provided in terms of its parameters. Most of these characterizations work without considering any additional requirement or assumption. Finally, as an application, a vectorial form of the Ekeland variational principle is provided.
A recorded video of the conference is here ; the slides can be downloaded here
Venue: Online via Google Meet meet.google.com/tta-bhpu-raa
A brief biography of the speaker: César Gutiérrez (ORCID iD 0000-0002-8223-2088) is Professor at Universidad of Valladolid (Spain) and researcher of the Mathematics Research Institute of the University of Valladolid (IMUVA). He is author of 54 papers on several subjects related to vector and set-valued optimization. Currently, he is Associate Editor of Optimization.
Principal-Agent problem in insurance: from discrete- to continuous-time
5 de October de 2020 Seminarfflores
Speaker: Doctor Nicolás Hernández
Center for Mathematical Modeling (CMM), Universidad de Chile, Santiago, Chile
Date: October 07, 2020 at 10:00
Title: Principal-Agent problem in insurance: from discrete-to continuous-time
Abstract: In this talk we present a contracting problem between an insurance buyer and the seller, subject to prevention efforts in the form of self-insurance and self-protection. We start with a static formulation, corresponding to an optimization problem with variational inequality constraint, and extend the main properties of the optimal contract to the continuous-time formulation, corresponding to a stochastic control problem in weak form under non-singular measures.
A recorded video of the conference is here; the slides can be downloaded here
Venue: Online via Google Meet here
A brief biography of the speaker: Nicolás Hernández is currently a Postdoctoral Researcher at the Center for Mathematical Modeling (CMM), at Universidad de Chile. He obtained his PhD in 2017, as a cotutelle between Université Paris-Dauphine and Universidad de Chile. His research areas of interest are Contract theory, stochastic control, mathematical finance, probability, optimization, game theory.
Sigma-convex functions and Sigma-subdifferentials
14 de September de 2020 Seminarfflores
Speaker: Prof. Mohammad Hossein Alizadeh
Institute for Advanced Studies in Basic Sciences (IASBS),
Zanjan, Iran
Date: September 23, 2020 at 10:00
Title: Sigma-convex functions and Sigma-subdifferentials
Abstract: In this talk we present and study the notion of $\sigma$-subdifferential of a proper function $f$ which contains the Clarke-Rockafellar subdifferential of $f$ under some mild assumptions on $f$.
We show that some well known properties of the convex function, namely Lipschitz property in the interior of its domain, remain valid for the large class of $\sigma$-convex functions.
Venue: Online via Google Meet meet.google.com/uoq-kifr-nsg
A brief biography of the speaker: Mohammad Hossein Alizadeh is an Assistant
Professor at the Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, Iran. He obtains his Ph.D. from the University the Aegean, Greece, in 2012. He is mainly interested in the following areas:
Monotone and generalized monotone operators, Monotone and generalized monotone
bifunctions, generalized convexity and generalized inverses.
Coordinators: Abderrahim Hantoute (CMM) and Fabián Flores-Bazán (Universidad de Concepción)
Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
26 de August de 2020 Seminarahantoute
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).
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.
An overview of Sweeping Processes with applications
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.
Epi-convergence, asymptotic analysis and stability in set optimization problems
3 de August de 2020 Seminarfflores
Speaker: Prof. Rubén López
University of Tarapacá, Arica, Chile
Title: Epi-convergence, asymptotic analysis and stability in set optimization problems
Abstract: We study the stability of set optimization problems with data that are not necessarily bounded. To do this, we use the well-known notion of epi-convergence coupled with asymptotic tools for set-valued maps. We derive characterizations for this notion that allows us to study the stability of vector and set type solutions by considering variations of the whole data (feasible set and objective map). We extend the notion of total epi-convergence to set-valued maps.
* This work has been supported by Conicyt-Chile under project FONDECYT 1181368
Joint work with Elvira Hérnández, Universidad Nacional de Educación a Distancia, Madrid, Spain
Venue: Online via Google Meet – https://meet.google.com/hgo-zwkr-fvh
A brief biography of the speaker: Prof. Rubén López is Professor at the University of Tarapacá, Arica – Chile. He studied at Moscow State University – Mech Math (1996, Russia) and Universidad de Concepción – DIM (2005, Chile). He works on Optimization: asymptotic analysis, variational convergences, stability theory, approximate solutions and well-posedness.
Satisfying Instead of Optimizing in the Nash Demand Games
15 de July de 2020 Seminarfflores
Speaker: Prof. Sigifredo Laengle
University of Chile, Santiago, Chile
Date: July 22, 2020 at 10:00
Abstract: The Nash Demand Game (NDG) has been one of the first models (Nash 1953) that has tried to describe the process of negotiation, competition, and cooperation. This model is still subject to active research, in fact, it maintains a set of open questions regarding how agents optimally select their decisions and how they face uncertainty. However, the agents act rather guided by chance and necessity, with a Darwinian flavor. Satisfying, instead of optimising. The Viability Theory (VT) has this approach. Therefore, we investigate the NDG under this point of view. In particular, we ask ourselves two questions: if there are decisions in the NDG that ensure viability and if this set also contains Pareto and equilibrium strategies. Thus, carrying out the work, we find that the answers to both questions are not only affirmative, but that we also advance in characterising viable NDGs. In particular, we conclude that a certain type of NDGs ensures viability and equilibrium. Many interesting questions originate from this initial work. For example, is it possible to fully characterise the NDG by imposing viability conditions? Under what conditions does viability require cooperation? Is extreme polarisation viable?
Venue: Online via Google Meet – meet.google.com/jhb-umew-kwp
A brief biography of the speaker: Prof. Sigifredo Laengle is an Associate Professor at the University of Chile since 2007. He received his PhD in Germany working on the theoretical problem of the value of information in organisations. He has published articles that articulate phenomena of strategic interaction, and optimisation.
Coordinators: Abderrahim Hantoute and Fabián Flores-Bazán (Universidad de Concepción)
Enlargements of the Moreau-Rockafellar Subdifferential
13 de July de 2020 Seminarahantoute
Speaker: Prof. Michel Théra
University of Limoges, France
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)
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