Expanding the applicability of the Gauss–Newton method for convex optimization under a majorant condition View Full Text


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Article Info

DATE

2014-06-24

AUTHORS

Á. Alberto Magreñán, Ioannis K. Argyros

ABSTRACT

A new semi-local convergence analysis of the Gauss–Newton method for solving convex composite optimization problems is presented using the concept of quasi-regularity for an initial point. Our convergence analysis is based on a combination of a center-majorant and a majorant function. The results extend the applicability of the Gauss–Newton method under the same computational cost as in earlier studies using a majorant function or Wang’s condition or Lipchitz condition. The special cases and applications include regular starting points, Robinson’s conditions, Smale’s or Wang’s theory. More... »

PAGES

37-56

References to SciGraph publications

  • 1995-12. A Gauss—Newton method for convex composite optimization in MATHEMATICAL PROGRAMMING
  • 1972-08. Extension of Newton's method to nonlinear functions with values in a cone in NUMERISCHE MATHEMATIK
  • 2008-09-03. Concerning the convergence of Newton’s method and quadratic majorants in JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
  • 2007-10-23. Kantorovich’s majorants principle for Newton’s method in COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • 1986. Newton’s Method Estimates from Data at One Point in THE MERGING OF DISCIPLINES: NEW DIRECTIONS IN PURE, APPLIED, AND COMPUTATIONAL MATHEMATICS
  • 2002-01. On convergence of the Gauss-Newton method for convex composite optimization in MATHEMATICAL PROGRAMMING
  • 2011-02-01. Extending the applicability of the Gauss–Newton method under average Lipschitz–type conditions in NUMERICAL ALGORITHMS
  • 1986-01. A Kantorovich-type convergence analysis for the Gauss-Newton-Method in NUMERISCHE MATHEMATIK
  • 1993. Convex Analysis and Minimization Algorithms II, Advanced Theory and Bundle Methods in NONE
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s40324-014-0018-5

    DOI

    http://dx.doi.org/10.1007/s40324-014-0018-5

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