Unconstrained Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds

G. C. Bento (), O. P. Ferreira () and P. R. Oliveira ()
Additional contact information
G. C. Bento: IME-Universidade Federal de Goiás
O. P. Ferreira: IME-Universidade Federal de Goiás
P. R. Oliveira: COPPE/Sistemas-Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 1, No 6, 88-107

Abstract: Abstract In this paper, we present a steepest descent method with Armijo’s rule for multicriteria optimization in the Riemannian context. The sequence generated by the method is guaranteed to be well defined. Under mild assumptions on the multicriteria function, we prove that each accumulation point (if any) satisfies first-order necessary conditions for Pareto optimality. Moreover, assuming quasiconvexity of the multicriteria function and nonnegative curvature of the Riemannian manifold, we prove full convergence of the sequence to a critical Pareto point.

Keywords: Steepest descent; Pareto optimality; Vector optimization; Quasi-Fejér convergence; Quasiconvexity; Riemannian manifolds (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-011-9984-2 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:154:y:2012:i:1:d:10.1007_s10957-011-9984-2

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

DOI: 10.1007/s10957-011-9984-2

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 ().