A modified Newton's method for minimizing factorable functions

Many functions of several variables used in nonlinear programming are factorable, i.e., complicated compositions of transformed sums and products of functions of a single variable. The Hessian matrices of twice-differentiable factorable functions can easily be expressed as sums of outer products (dyads) of vectors. A modified Newton's method for minimizing unconstrained factorable functions which exploits this special form of the Hessian is developed. Computational experience with the method is presented.This material is based upon work supported by the National Science Foundation under Grant No. MCS-79-04106.The author would like to thank Professor G. P. McCormick, George Washington University, for several enlightening discussions on factorable programming and for his valuable comments which improved an earlier version of this paper.