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

  • Authors:

  • J. X. Cruz Neto;O. P. Ferreira;L. R. Pérez;S. Z. Németh

  • Affiliations:

  • DM, Universidade Federal do Piauí, Teresina, BR 64049-500;IME, Universidade Federal de Goiás, Goiânia, BR 74001-970;IME, Universidade Federal de Goiás, Goiânia, BR 74001-970;Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary 1518

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2006

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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.