Editorial: A special issue dedicated to Franco Giannessi
Journal of Nonlinear and Variational Analysis · 2020
It is our immense pleasure to dedicate this special issue to Professor Franco Giannessi on the occasion of his 85th birthday.Prof. Giannessi's profound and original ideas influenced and shaped various research directions in variational analysis and mathematical optimization over many decades.He pioneered the notion of vector variational inequalities, which is now an important branch of applied mathematics.He independently discovered the powerful mathematical tool called the image space approach, strengthened it, and addressed crucial applications employing it.There are essential results available in optimization, control, equilibrium problems, and variational and quasi-variational inequalities that have been derived by using the mechanism of the image space analysis.He also proposed the notion of the now so-called G-semi-differentiability of a function.This special issue aims to acknowledge and celebrate his beautiful ideas and novel contributions as an innovative researcher of the highest caliber.This special issue is comprised of ten articles whose contributions are as follows: G. Mastroeni, M. Pappalardo, and F. Raciti, in the paper "Some topics in vector optimization via image space analysis," provide an excellent introduction to the image space analysis in the context of a vector optimization problem, and its use in proving specific existence results.They also give various separation schemes and discuss their impact on deriving optimality conditions.An exposition to the notion of G-semi-differentiability of a function is also given.B. Ricceri, in the article "A remark on variational inequalities in small balls," proves new existence results for variational inequalities and the associated Minty formulation given on small closed balls.The primary focus of the paper, "Nonsmooth dynamics of generalized Nash games" by T. Migot and M. Cojocaru, is to study the generalized Nash equilibrium problem using quasi-variational inequalities in a dynamical system framework.The authors provide a nice introduction to variational inequalities, projected dynamical systems, and equilibrium problems and relate the generalized Nash equilibrium problem to nonsmooth dynamical systems.They provide examples to illustrate the key challenges in handing the underlying variable constraint sets.New existence results are given for the considered dynamical system.The authors propose two classes of algorithms and test them on applied models.The goal of the work "A projected dynamic system associated with a cybersecurity investment model with budget constraints and fixed demands" by G. Colajanni, P. Daniele, and D. Sciacca is to investigate a network-based cybersecurity investment model with nonlinear budget constraints and fixed demands.The authors use the average value of the security levels for the supply chain network as a weighted