Journal of Global Optimization

, Volume 35, Issue 1, pp 53–69 | Cite as

Convex- and Monotone-Transformable Mathematical Programming Problems and a Proximal-Like Point Method

  • J. X. Da Cruz Neto
  • O. P. Ferreira
  • L. R. Lucambio Pérez
  • S. Z. Németh
Article

Abstract

The problem of finding the singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will also be shown how tools of convex analysis on Riemannian manifolds can solve non-convex constrained problems in Euclidean spaces. To illustrate this remarkable fact examples will be given.

Keywords

Manifold Vector Field Riemannian Manifold Euclidean Space Programming Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • J. X. Da Cruz Neto
    • 1
  • O. P. Ferreira
    • 2
  • L. R. Lucambio Pérez
    • 2
  • S. Z. Németh
    • 3
  1. 1.DMUniversidade Federal do PiauíTeresinaBR
  2. 2.IMEUniversidade Federal de GoiásGoiâniaBR
  3. 3.Computer and Automation InstituteHungarian Academy of SciencesBudapestHungary

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