Critical point index for vector functions and vector optimization

Enrico Miglierina, E. Miglierina, E. Molho, M. Rocca

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)479-496
Number of pages18
JournalJournal of Optimization Theory and Applications
Publication statusPublished - 2008


  • Critical points
  • Morse index
  • Second-order differentials
  • Vector optimization

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