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)