Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 48, Issue 1, Pages 1-29Publisher
SIAM PUBLICATIONS
DOI: 10.1137/080732432
Keywords
nonlinear least-squares; systems of nonlinear equations; numerical algorithms; global convergence
Categories
Funding
- MIUR
- GNCS/INDAM
- EPSRC [EP/F005369/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/F005369/1] Funding Source: researchfish
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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 sub-problem 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.
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