Automatic Determination of an Initial Trust Region in Nonlinear Programming
SIAM Journal on Scientific Computing
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
Solving the Trust-Region Subproblem using the Lanczos Method
SIAM Journal on Optimization
Minimizing a Quadratic Over a Sphere
SIAM Journal on Optimization
GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
ACM Transactions on Mathematical Software (TOMS)
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Cubic regularization of Newton method and its global performance
Mathematical Programming: Series A and B
Finding Optimal Algorithmic Parameters Using Derivative-Free Optimization
SIAM Journal on Optimization
Affine conjugate adaptive Newton methods for nonlinear elastomechanics
Optimization Methods & Software
Iterative Methods for Finding a Trust-region Step
SIAM Journal on Optimization
A Subspace Minimization Method for the Trust-Region Step
SIAM Journal on Optimization
Convergence of a Regularized Euclidean Residual Algorithm for Nonlinear Least-Squares
SIAM Journal on Numerical Analysis
Mathematical Programming: Series A and B
Complexity bounds for second-order optimality in unconstrained optimization
Journal of Complexity
Mathematical Programming: Series A and B
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The adaptive cubic regularization method (Cartis et al. in Math. Program. Ser. A 127(2):245---295, 2011; Math. Program. Ser. A. 130(2):295---319, 2011) has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regularization parameter whose role is related to the local Lipschitz constant of the objective's Hessian. We present new updating strategies for this parameter based on interpolation techniques, which improve the overall numerical performance of the algorithm. Numerical experiments on large nonlinear least-squares problems are provided.