<![CDATA[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 computedof its inverse which make the solution is very expensive. In this work we will updating the LU factors of theHessian matrix so we dont need to compute the inverse of Hessian matrix, so called the Cholesky Update forunconstrained optimization. We introduce the convergent of the update and report our findings on severalstandard problems, and make a comparison on its performance with the well-accepted BFGS update.Key words: Unconstrained Optimization, Cholesky factorization, convergence]]>
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