Extending the applicability of Gauss-Newton method for convex composite optimization on Riemannian manifolds

  1. Argyros, I.K. 1
  2. Magreñán, A.A. 2
  1. 1 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Año de publicación: 2014

Volumen: 249

Páginas: 453-467

Tipo: Artículo

DOI: 10.1016/J.AMC.2014.09.119 SCOPUS: 2-s2.0-84911436804 WoS: WOS:000345579500045 GOOGLE SCHOLAR

Otras publicaciones en: Applied Mathematics and Computation

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Resumen

We present a semi-local convergence analysis of the Gauss-Newton method for solving convex composite optimization problems in Riemannian manifolds using the notion of quasi-regularity for an initial point. Using a combination the L-average Lipszhitz condition and the center L0-average Lipschitz condition we introduce majorizing sequences for the Gauss-Newton method that are more precise than in earlier studies. Consequently, our semi-local convergence analysis for the Gauss-Newton method has the following advantages under the same computational cost: weaker sufficient convergence conditions; more precise estimates on the distances involved and an at least as precise information on the location of the solution.