Principal-Agent problem in insurance: from discrete- to continuous-time

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.

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

Sigma-convex functions and Sigma-subdifferentials

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.

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

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

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)

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.

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

Epi-convergence, asymptotic analysis and stability in set optimization problems

Speaker: Prof. Rubén López
University of Tarapacá, Arica, Chile

Date:  August 05, 2020 at 10:00

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

The slides of the conference can be downloaded here

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.

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

Satisfying Instead of Optimizing in the Nash Demand Games

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?

The slides of the conference can be downloaded here

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

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)

A general asymptotic function with applications

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)

Characterizing the calmness property in convex semi-infinite optimization. Modulus estimates.

Speaker: Prof. Marco Antonio López Cerdá
University of Alicante, Spain

Date: Jun 03, 2020 at 10:00

Abstract: We present an overview of the main results on calmness in convex
semi-infinite optimization. The first part addresses the calmness of the
feasible set and the optimal set mappings for the linear semi-infinite
optimization problem in the setting of canonical perturbations, and also
in the framework of full perturbations. While there exists a clear
proportionality between the calmness moduli of the feasible set mappings
in both contexts, the analysis of the relationship between the calmness
moduli of the argmin mappings is much more complicated. Point-based
expressions (only involving the nominal problem’s data) for the calmness
moduli are provided. The second part focuses on convex semi-infinite
optimization, and provides a characterization of the Hölder calmness of
the optimal set mapping, by showing its equivalence with the Hölder
calmness of a certain (lower) level set mapping.

The slides of the conference can be downloaded here.

Venue: Online via Google Meet – https://meet.google.com/jps-drzk-jjd

A brief biography of the speaker: Prof. Marco A. López-Cerdá received his education in Mathematics from Valencia University (graduate in 1971, doctor in 1973). In 1981 became Full Professor in Operations Research (OR, in brief); in 1985 moved to Alicante University, where is Emeritus Professor since September of 2019. Adjunct Professor of the Centre for Informatics and Applied Optimization (CIAO) at Federation University Australia (since 2013). Doctor Honoris Causa by the University of Limoges (July, 2012), and Corresponding Member of the Spanish Real Academia de Ciencias. (Co)advisor of 17 Ph.D. students in several branches of OR such as semi-infinite programming, network flows, assignment problem, convex optimization, graphs, scheduling, game theory and variational analysis. His 1998 book (with M.A. Goberna) Linear Semi-Infinite Optimization is considered a classical in the field. 147 papers published (according to MathSciNet) in first-rank journals as Math. Programming, MOR, SIOPT, JOTA, Optimization, etc. His publications have been cited 1595 times by 543 authors (again according to MathSciNet). Other positions related to the OR community are: (co-)editor in chief of TOP (the OR journal of SEIO, the Spanish Society of Statistics and Operations Research) from 2000 to 2007, elected president of SEIO in 1986, chair of EUROPT in the period 2008-2010, coordinator of i-MATH Consolider (2006-2011), a huge research program of the Spanish Ministry of Education for all areas of mathematics, Associate Editor in JOTA, JIMO, RACSAM, SVVA, etc.

 

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