Least-Squares Minimization Under Constraints

Unconstrained Least-Squares minimization is a well-studied problem. For example, the Levenberg-Marquardt is extremely effective and numerous implementations are readily available. These algorithms are, however, not designed to perform least-squares minimization under hard constraints. This short report outlines two very simple approaches to doing this. The first relies on standard Lagrange multipliers. The second is inspired by inverse kinematics techniques.