Nonlinear Programming Methods with Linear Least Squares Subproblems

This paper presents the results of an extensive comparative study of nonlinear optimization algorithms, cf. [8]. This study indicates that quadratic approximation methods,which are characterizéd by solving a sequence of quadratic subproblems recursively, belong to the most efficient and reliable nonlinear programming algorithms available at present. The purpose of the paper is to investigate their numerical performance in more detail. In particular, the dependence of the overall performance on alternative quadratic subproblem strategies is tested. The paper indicates how the efficiency of quadratic approximate methods can be improved.