Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 343-360
Generic well-posedness in minimization problems
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