Interior point algorithms for nonlinear constrained least squares problems

Abstract

We consider Nonlinear Least Squares problems with equality and inequality constraints and propose a numerical technique that integrates methods for unconstrained problems, based on Gauss-Newton algorithm, with FAIPA, the Feasible Arc Interior Point Algorithm for constrained optimization. We also present some numerical results on test problems available in the literature and compare them with the quasi-Newton version of FAIPA. We also describe an application to the identification of mechanical parameters of composite materials. The present algorithms are globally convergent, very robust and efficient.