Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
Journal of Optimization Theory and Applications
Factorized quasi-Newton methods for nonlinear least squares problems
Mathematical Programming: Series A and B
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
A modified BFGS method and its global convergence in nonconvex minimization
Journal of Computational and Applied Mathematics - Special issue on nonlinear programming and variational inequalities
On the Global Convergence of the BFGS Method for Nonconvex Unconstrained Optimization Problems
SIAM Journal on Optimization
A Family of Scaled Factorized Broyden-Like Methods for Nonlinear Least Squares Problems
SIAM Journal on Optimization
Convergence Properties of the BFGS Algoritm
SIAM Journal on Optimization
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Approximate Gauss-Newton Methods for Nonlinear Least Squares Problems
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 0.00 |
In this paper, we propose a hybrid Gauss-Newton structured BFGS method with a new update formula and a new switch criterion for the iterative matrix to solve nonlinear least squares problems. We approximate the second term in the Hessian by a positive definite BFGS matrix. Under suitable conditions, global convergence of the proposed method with a backtracking line search is established. Moreover, the proposed method automatically reduces to the Gauss-Newton method for zero residual problems and the structured BFGS method for nonzero residual problems in a neighborhood of an accumulation point. A locally quadratic convergence rate for zero residual problems and a locally superlinear convergence rate for nonzero residual problems are obtained for the proposed method. Some numerical results are given to compare the proposed method with some existing methods.