The convergence properties of the new regularized Euclidean residual method for solving general nonlinear least-squares and nonlinear equation problems are investigated. This method, derived from a proposal by Nesterov [Optim. Methods Softw., 22 (2007), pp. 469–483], uses a model of the objective function consisting of the unsquared Euclidean linearized residual regularized by a quadratic term. At variance with previous analysis, its convergence properties are here considered without assuming uniformly nonsingular globally Lipschitz continuous Jacobians nor an exact subproblem solution. It is proved that the method is globally convergent to first-order critical points and, under stronger assumptions, to roots of the underlying system of nonlinear equations. The rate of convergence is also shown to be quadratic under stronger assumptions.

Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares / S. Bellavia; C. Cartis; N. I. M. Gould; B. Morini; Ph. L. Toint;. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 48:(2010), pp. 1-29. [10.1137/080732432]

Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares

BELLAVIA, STEFANIA;MORINI, BENEDETTA;
2010

Abstract

The convergence properties of the new regularized Euclidean residual method for solving general nonlinear least-squares and nonlinear equation problems are investigated. This method, derived from a proposal by Nesterov [Optim. Methods Softw., 22 (2007), pp. 469–483], uses a model of the objective function consisting of the unsquared Euclidean linearized residual regularized by a quadratic term. At variance with previous analysis, its convergence properties are here considered without assuming uniformly nonsingular globally Lipschitz continuous Jacobians nor an exact subproblem solution. It is proved that the method is globally convergent to first-order critical points and, under stronger assumptions, to roots of the underlying system of nonlinear equations. The rate of convergence is also shown to be quadratic under stronger assumptions.
48
1
29
S. Bellavia; C. Cartis; N. I. M. Gould; B. Morini; Ph. L. Toint;
File in questo prodotto:
File Dimensione Formato  
SINUM_RER.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: DRM non definito
Dimensione 348.89 kB
Formato Adobe PDF
348.89 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/368307
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 32
  • ???jsp.display-item.citation.isi??? 30
social impact