Generic well-posedness in minimization problems. (English) Zbl 1099.49023

Ioffe, A.; Lucchetti, R. E.

Abstr. Appl. Anal. 2005, No. 4, 343-360 (2005).

This paper provides an overview of several results concerning genericity properties, in various settings, of well-posed scalar optimization problems. Genericity of Tikhonov well-posedness and well-posedness under perturbations is examined. Moreover, porosity results are described with applications to convex programming problems.

Reviewer: Tullio Zolezzi (Genova)

MSC:

49K40	Sensitivity, stability, well-posedness
49J27	Existence theories for problems in abstract spaces
90C25	Convex programming

Keywords:

well-posed optimization problems; Tikhonov well-posedness