The present paper contains a study of covering (alias, openness) properties at a nonlinear rate for set-valued mappings between metric spaces. Such study is focussed on the stability of these properties in the presence of perturbations. A crucial result valid for linear openness, known as Milyutin's theorem, is extended to set-valued mappings covering at a nonlinear rate under possibly non-Lipschitz perturbations. Consequently, a Lyusternik type theorem is derived from such extension and a general penalization principle for constrained optimization problems, which exploits nonlinear covering properties, is presented. © 2011 Elsevier Ltd. All rights reserved.
Uderzo, A. (2012). On mappings covering at a nonlinear rate and their perturbation stability. NONLINEAR ANALYSIS, 75(3), 1602-1616 [10.1016/j.na.2011.03.014].
On mappings covering at a nonlinear rate and their perturbation stability
UDERZO, AMOS
2012
Abstract
The present paper contains a study of covering (alias, openness) properties at a nonlinear rate for set-valued mappings between metric spaces. Such study is focussed on the stability of these properties in the presence of perturbations. A crucial result valid for linear openness, known as Milyutin's theorem, is extended to set-valued mappings covering at a nonlinear rate under possibly non-Lipschitz perturbations. Consequently, a Lyusternik type theorem is derived from such extension and a general penalization principle for constrained optimization problems, which exploits nonlinear covering properties, is presented. © 2011 Elsevier Ltd. All rights reserved.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
