In this work, we study the critical points of vector functions from R^n to R^m with n ≥ m, following the definition introduced by Smale in the context of vector optimization. The local monotonicity properties of a vector function around a critical point which are invariant with respect to local coordinate changes are considered. We propose a classification of critical points through the introduction of a generalized Morse index for a critical point, consisting of a triplet of nonnegative integers. The proposed index is based on the sign of an appropriate invariant vector-valued second order differential.
Critical point index for vector functions and vector optimization
MIGLIERINA, ENRICO;MOLHO, ELENA;ROCCA, MATTEO
2008-01-01
Abstract
In this work, we study the critical points of vector functions from R^n to R^m with n ≥ m, following the definition introduced by Smale in the context of vector optimization. The local monotonicity properties of a vector function around a critical point which are invariant with respect to local coordinate changes are considered. We propose a classification of critical points through the introduction of a generalized Morse index for a critical point, consisting of a triplet of nonnegative integers. The proposed index is based on the sign of an appropriate invariant vector-valued second order differential.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.