Majorization-Minimization-Based Levenberg--Marquardt Method for Constrained Nonlinear Least Squares

Understand

A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described.

• Various versions of the LM method have been proposed, their main differences being in the choice of a damping parameter.
• In this paper, we propose a new rule for updating the parameter so as to achieve both global and local convergence even under the presence of a convex constraint set.
• The key to our results is a new perspective of the LM method from majorization-minimization methods.