Journal of Global Optimization

, Volume 31, Issue 1, pp 133–151

Singularities of Monotone Vector Fields and an Extragradient-type Algorithm

  • O. P. Ferreira
  • L. R. Lucambio. Pérez
  • S. Z. Németh
Article

DOI: 10.1007/s10898-003-3780-y

Cite this article as:
Ferreira, O.P., Pérez, L.R.L. & Németh, S.Z. J Glob Optim (2005) 31: 133. doi:10.1007/s10898-003-3780-y

Abstract.

Bearing in mind the notion of monotone vector field on Riemannian manifolds, see [12--16], we study the set of their singularities and for a particularclass of manifolds develop an extragradient-type algorithm convergent to singularities of such vector fields. In particular, our method can be used forsolving nonlinear constrained optimization problems in Euclidean space, with a convex objective function and the constraint set a constant curvature Hadamard manifold. Our paper shows how tools of convex analysis on Riemannian manifolds can be used to solve some nonconvex constrained problem in a Euclidean space.

Keywords

extragradient algorithm global optimization Hadamard manifold monotone vector field 

Copyright information

© Springer Science+Business Media New York 2005

Authors and Affiliations

  • O. P. Ferreira
    • 1
  • L. R. Lucambio. Pérez
    • 1
  • S. Z. Németh
    • 2
  1. 1.IMEUniversidade Federal de GoiásGoâniaBrazil
  2. 2.Computer and Automation InstituteHungarian Academy of SciencesHungary

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