The Numerical Solution of Constrained Linear Least-squares Problems

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Abstract
The paper describes a numerically stable algorithm to solve constrained linear least-squares problems and allows rank deficient or underdetermined observation matrices. The method starts with the calculation of the rank of the observation matrix and the transformation into a least distance problem. The proposed technique for solving the least distance problem can be considered as a generalization of the projection method of Stoer (1971). Starting with a feasible point, a sequence of iterates is calculated by minimizing the objective function on the linear boundary manifold determined by the active constraints. Numerical examples show the feasibility of the algorithm.

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