Steepest descent method with a generalized Armijo search for quasiconvex functions on Riemannian manifolds

E. A. Papa Quiroz, E. M. Quispe, P. Roberto Oliveira

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23 Scopus citations

Abstract

This paper extends the full convergence of the steepest descent method with a generalized Armijo search and a proximal regularization to solve minimization problems with quasiconvex objective functions on complete Riemannian manifolds. Previous convergence results are obtained as particular cases and some examples in non-Euclidian spaces are given. In particular, our approach can be used to solve constrained minimization problems with nonconvex objective functions in Euclidian spaces if the set of constraints is a Riemannian manifold and the objective function is quasiconvex in this manifold.

Original languageEnglish
Pages (from-to)467-477
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume341
Issue number1
DOIs
StatePublished - 1 May 2008

Keywords

  • Quasiconvex functions
  • Riemannian manifolds
  • Steepest descent method

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