Use of a Stable Generalized Inverse Algorithm to Evaluate Newton Method Strategies,

摘要

Modifications of Newton's method for minimizing an unconstrained function are presented. A numerically stable matrix factorization is given for obtaining the generalized inverse of an approximation to the positive part of the Hessian matrix and directions of nonpositive curvature. Three different modified Newton strategies are interfaced with the computer program SUMT which transforms a constrained minimization problem into a sequence of unconstrained problems. Numerical evaluation of these three strategies is given for a variety of test problems. (Author)