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

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.
Vector optimization · Critical points · Morse index · Second-order differentials
Miglierina, Enrico; Molho, Elena; Rocca, Matteo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11383/1671142
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