A primal-dual interior-point algorithm for nonlinear least squares constrained problems

Abstract

This paper extends prior work by the authors on solving nonlinear least squares unconstrained problems using a factorized quasi-Newton technique. With this aim we use a primal-dual interior-point algorithm for nonconvex nonlinear program- ming. The factorized quasi-Newton technique is now applied to the Hessian of the Lagrangian function for the transformed problem which is based on a logarithmic barrier formulation. We emphasize the importance of establishing and maintaining symmetric quasi-definiteness of the reduced KKT system. The algorithm then tries to choose a step size that reduces a merit function, and to select a penalty parameter that ensures descent directions along the iterative process. Computa- tional results are included for a variety of least squares constrained problems and preliminary numerical testing indicates that the algorithm is robust and efficient in practice.