BibTeX
@ARTICLE{
         Arora2004Atr,
       title = "A trust region {SQP} algorithm for equality constrained parameter estimation with
         simple parameter bounds",
       author = "Nikhil Arora and Lorenz T. Biegler",
       publisher = "Springer",
       year = "2004",
       journal = "Computational Optimization and Applications",
       volume = "28",
       pages = "51--86",
       doi = "10.1023/B:COAP.0000018879.40214.11",
       abstract = "We describe a new algorithm for a class of parameter estimation problems, which are
         either unconstrained or have only equality constraints and bounds on parameters. Due to the presence
         of unobservable variables, parameter estimation problems may have non-unique solutions for these
         variables. These can also lead to singular or ill-conditioned Hessians and this may be responsible
         for slow or non-convergence of nonlinear programming (NLP) algorithms used to solve these problems.
         For this reason, we need an algorithm that leads to strong descent and converges to a stationary
         point. Our algorithm is based on Successive Quadratic Programming (SQP) and constrains the SQP steps
         in a trust region for global convergence. We consider the second-order information in three ways:
         quasi-Newton updates, Gauss-Newton approximation, and exact second derivatives, and we compare their
         performance. Finally, we provide results of tests of our algorithm on various problems from the CUTE
         and COPS sets",
       ad_area = "Chemistry",
       ad_tools = "ADOL-C",
       ad_theotech = "Hessian"
}