Linear Least Squares with Bounds and Linear Constraints

Abstract

An algorithm is given for solving linear least squares systems of algebraic equations subject to simple bounds on the unknowns and (more general) linear equality and inequality constraints. The method used is a penalty function approach wherein the linear constraints are (effectively) heavily weighted. The resulting system is then solved as an ordinary bounded least squares system except for some important numerical and algorithmic details. This report is a revision of an earlier work. It reflects some hard-won experience gained while using the resulting software to solve nonlinear constrained least squares problems.