Critical Points Index for Vector Functions and Vector Optimization

E. Miglierina (), E. Molho () and M. Rocca ()
Additional contact information
E. Miglierina: University of Insubria
E. Molho: University of Pavia
M. Rocca: University of Insubria

Journal of Optimization Theory and Applications, 2008, vol. 138, issue 3, No 10, 479-496

Abstract: 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.

Keywords: Vector optimization; Critical points; Morse index; Second-order differentials (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-008-9383-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:138:y:2008:i:3:d:10.1007_s10957-008-9383-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-008-9383-5

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().