Linear least squares with bounds and liner constraints
SIAM Journal on Scientific and Statistical Computing
ACM SIGNUM Newsletter
The use of linear programming for the solution of sparse sets of nonlinear equations
SIAM Journal on Scientific and Statistical Computing
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4]
ACM Transactions on Mathematical Software (TOMS)
On developing mathematical software
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Letter to the Editor: On developing mathematical software
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
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A new algorithm is presented for solving nonlinear least-squares and nonlinear equation problems. The algorithm is based on approximating the nonlinear functions using the quadratic-tensor model proposed by Schnabel and Frank. The problem statement may include simple bounds or more general linear constraints on the unknowns. The algorithm uses a trust-region defined by a box containing the current values of the unknowns. The objective function (Euclidean length of the functions) is allowed to increase at intermediate steps. These increases are allowed as long as our predictor indicates that a new set of best values exists in the trust-region. There is logic provided to retreat to the current best values, should that be required. The computations for the model-problem require a constrained nonlinear least-squares solver. This is done using a simpler version of the algorithm. In its present form the algorithm is effective for problems with linear constraints and dense Jacobian matrices. Results on standard test problems are presented in the Appendix. The new algorithm appears to be efficient in terms of function and Jacobian evaluations.