Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 343-360

Generic well-posedness in minimization problems

A. Ioffe1 and R. E. Lucchetti2

1Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
2Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 7, Milano 20133, Italy

Received 12 February 2004

Copyright © 2005 A. Ioffe and R. E. Lucchetti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The goal of this paper is to provide an overview of results concerning, roughly speaking, the following issue: given a (topologized) class of minimum problems, “how many” of them are well-posed? We will consider several ways to define the concept of “how many,” and also several types of well-posedness concepts. We will concentrate our attention on results related to uniform convergence on bounded sets, or similar convergence notions, as far as the topology on the class of functions under investigation is concerned.