scholarly journals Convergence theory for the structured BFGS secant method with an application to nonlinear least squares

1989 ◽  
Vol 61 (2) ◽  
pp. 161-178 ◽  
Author(s):  
J. E. Dennis ◽  
H. J. Martinez ◽  
R. A. Tapia
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Secant Method ◽  
Convergence Theory

scholarly journals Newton-Krylov Type Algorithm for Solving Nonlinear Least Squares Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Mohammedi R. Abdel-Aziz ◽  
Mahmoud M. El-Alem
Keyword(s):  
Least Squares ◽  
Original Problem ◽  
Krylov Subspace ◽  
Quadratic Function ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Dimensional Subspace ◽  
Convergence Theory ◽  
Least Squares Problems ◽  
Programming Algorithms

The minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming algorithms. When the number of variables is large, one of the most widely used strategies is to project the original problem into a small dimensional subspace. In this paper, we introduce an algorithm for solving nonlinear least squares problems. This algorithm is based on constructing a basis for the Krylov subspace in conjunction with a model trust region technique to choose the step. The computational step on the small dimensional subspace lies inside the trust region. The Krylov subspace is terminated such that the termination condition allows the gradient to be decreased on it. A convergence theory of this algorithm is presented. It is shown that this algorithm is globally convergent.

Gauss‐Newton‐Secant method for solving nonlinear least squares problems

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Roman Iakymchuk ◽  
Halyna Yarmola ◽  
Stepan Shakhno
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Secant Method ◽  
Least Squares Problems
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