In this work, we study the critical points of vector functions from Rn to Rm 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 points index for vector functions and vector optimization
MOLHO, ELENA;
2008-01-01
Abstract
In this work, we study the critical points of vector functions from Rn to Rm 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.File in questo prodotto:
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