The dimension of semialgebraic subdifferential graphs

A corollary of a celebrated theorem of Minty is that the subdifferential graph of a closed convex function on R n has uniform local dimension n . In contrast, there exist nonconvex closed functions whose subdifferentials have large graphs. We consider how far Minty’s corollary extends to functions t...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Nonlinear analysis 2012-02, Vol.75 (3), p.1231-1245
Hauptverfasser:	Drusvyatskiy, D., Ioffe, A.D., Lewis, A.S.
Format:	Artikel
Sprache:	eng
Schlagworte:	Dimension Exact sciences and technology Graphs Manifolds and cell complexes Mathematical analysis Mathematics Nonlinearity Sciences and techniques of general use Semi-algebraic Set-valued map Stratification Subdifferential Theorems Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	A corollary of a celebrated theorem of Minty is that the subdifferential graph of a closed convex function on R n has uniform local dimension n . In contrast, there exist nonconvex closed functions whose subdifferentials have large graphs. We consider how far Minty’s corollary extends to functions that are nonconvex but semi-algebraic.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2011.07.040