Gauss-Newton Based Algorithms For Constrained Nonlinear Least Squares Problems

Abstract

This paper has two main purposes: To discuss general principles for a reliable and efficient numerical method based on the linearizations given in (2) and (3) and to present algorithms for which we have developed software. Our practical experience of methods of this kind are closely related to and, to some extent, limited by the experimentation needed to derive that software. Still there are two features which, we think, should be included in most algorithms based on the linearizations (2) and (3): 1) If the least squares problem turns out to have a large relative residual close to the solution - see the definition in section 2.8 - there has to be a switch to a method that incorporates second order information. The algorithm should in this sense be a hybrid algorithm. 2) It seems to be both convenient and natural to use line search on a quadratic merit function for a constrained nonlinear least squares problem. The merit function will be described and investigated in section 4. 1.1 Equality constrained problem