THE CHOLESKY UPDATE FOR UNCONSTRAINED OPTIMIZATION

Abstract

It is well known that the unconstrained Optimization often arises in economies, finance, trade, law, meteorology, medicine, biology, chemistry, engineering, physics, education, history, sociology, psychology, and so on. The classical Unconstrained Optimization is based on the Updating of Hessian matrix and computed of its inverse which make the solution is very expensive. In this work we will updating the LU factors of the Hessian matrix so we don’t need to compute the inverse of Hessian matrix, so called the Cholesky Update for unconstrained optimization. We introduce the convergent of the update and report our findings on several standard problems, and make a comparison on its performance with the well-accepted BFGS update.