ALGORITHM-739 - A SOFTWARE PACKAGE FOR UNCONSTRAINED OPTIMIZATION USING TENSOR METHODS

This paper describes a software package for finding the unconstrained minimizer of a nonlinear function of n variables. The package is inten ded for problems where n is not too large-say, n < 100-so that the cos t of storing one n X n matrix, and factoring it at each iteration, is acceptable. The software allows the user to choose between a recently developed ''tensor method'' for unconstrained optimization and an anal ogous standard method based on a quadratic model. The tenser method ba ses each iteration on a specially constructed fourth-order model of th e objective function not significantly more expensive to form, store, or solve than the standard quadratic model. In our experience, the ten ser method requires significantly fewer iterations and function evalua tions to solve most unconstrained optimization problems than standard methods based on quadratic models, and also solves a somewhat wider ra nge of problems. For these reasons, it may be a useful addition to num erical software libraries.