More test examples for nonlinear programming codes
More test examples for nonlinear programming codes
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
On the convegence of a sequential penalty function method for constrained minimization
SIAM Journal on Numerical Analysis
Journal of Optimization Theory and Applications
A constrained least squares regularization method for nonlinear ill-posed problems
SIAM Journal on Control and Optimization
SIAM Journal on Numerical Analysis
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4]
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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An iterative method for solving the nonlinear minimization problem with equality constraints is presented. The method is based on the sequential minimization of the augmented Lagrangian function. The unconstrained minimization subproblems are solved by using a technique based on the conjugate gradients combined with the trust region approach as globalization strategy. The Hessian matrix of the augmented Lagrangian is updated by using a BFGS-like structured secant approximation. Global convergence results are shown. The method is applied to solve the equality constrained nonlinear least squares problem. Numerical results are presented not only with well-known test problems but also with ill-posed problems involving a regularization. Even though the tested problems are small and medium, features like the conjugate gradient/trust region strategy and the structured secant approximation make the proposed algorithm specially efficient for large scale problems.