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.
Lingua originale | English |
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pagine (da-a) | 479-496 |
Numero di pagine | 18 |
Rivista | Journal of Optimization Theory and Applications |
Volume | 138 |
DOI | |
Stato di pubblicazione | Pubblicato - 2008 |
Keywords
- Critical points
- Morse index
- Second-order differentials
- Vector optimization