Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 343-360
doi:10.1155/AAA.2005.343
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
Abstract
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.