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)

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)

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)