NLPLSQ: a Fortran implementation of an SQP-Gauss-Newton algorithm for least squares optimization. The Fortran subroutine NLPLSQ solves constrained least squares nonlin- ear programming problems, where the sum of squared nonlinear functions is to be minimized. It is assumed that all functions are continuously differentiable. By introducing additional variables and nonlinear equality constraints, the problem is transformed into a general smooth nonlinear program subsequently solved by the sequential quadratic programming (SQP) code NLPQLP. It can be shown that typical features of special purpose algorithms are retained, i.e., a combination of a Gauss-Newton and a quasi-Newton search direction. The additionally introduced variables are eliminated in the quadratic programming subproblem, so that calculation time is not increased significantly. Some com- parative numerical results are included, the usage of the code is documented, and two illustrative examples are presented.

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  1. Orban, Dominique; Siqueira, Abel Soares: A regularization method for constrained nonlinear least squares (2020)