Continuity of the null space basis and constrained optimization
Mathematical Programming: Series A and B
How bad are the BFGS and DFP methods when the objective function is quadratic?
Mathematical Programming: Series A and B
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Steplength algorithms for minimizing a class of nondifferentiable functions
Steplength algorithms for minimizing a class of nondifferentiable functions
Handling degeneracy in a nonlinear l(,1) algorithm
Handling degeneracy in a nonlinear l(,1) algorithm
Solution of nonlinear least-squares problems
Solution of nonlinear least-squares problems
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This paper is concerned with the development, numerical implementation, and testing of an algorithm for solving constrained nonlinear least squares problems. The algorithm is an adaptation of the least squares case of an exact penalty method for solving nonlinearly constrained optimization problems due to Coleman and Conn. It also uses the ideas of Nocedal and Overton for handling quasi-Newton updates of projected Hessians, those of Dennis, Gay, and Welsch for approaching the structure of nonlinear least squares Hessians, and those of Murray and Overton for performing line searches. This method has been tested on a selection of problems listed in the collection of Hock and Schittkowski. The results indicate that the approach taken here is a viable alternative for least squares problems to the general nonlinear methods studied by Hock and Schittkowski.