An Inexact Steepest Descent Method for Multicriteria Optimization on Riemannian Manifolds

G. C. Bento (), J. X. Cruz Neto () and P. S. M. Santos ()
Additional contact information
G. C. Bento: Universidade Federal de Goiás
J. X. Cruz Neto: Universidade Federal Piauí
P. S. M. Santos: Universidade Federal Piauí

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 1, No 6, 108-124

Abstract: Abstract In this paper, we present an inexact version of the steepest descent method with Armijo’s rule for multicriteria optimization in the Riemannian context given in Bento et al. (J. Optim. Theory Appl., 154: 88–107, 2012). 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 that the multicriteria function is quasi-convex and the Riemannian manifold has nonnegative curvature, we show full convergence of any sequence generated by the method to a Pareto critical point.

Keywords: Steepest descent; Pareto optimality; Multicriteria optimization; Quasi-Fejér convergence; Quasi-convexity; Riemannian manifolds (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0305-9 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:159:y:2013:i:1:d:10.1007_s10957-013-0305-9

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

DOI: 10.1007/s10957-013-0305-9

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 ().