A Modified Newton’s Method for Unconstrained Minimization

Abstract

Newton’s method for the minimization of a function of several variables presents difficulties in the case where the Hessian matrix is not positive definite. Various modifications are known. Any such modification uses a factorization of the Hessian. This paper suggests using the symmetric decomposition established in an earlier paper by the same authors [7]. The direction of descent is then chosen in a natural and simple manner. The resulting algorithm competes well with other variations. Numerical results are also included.