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)