Abstract: Duetotheadvantagesofthequadraticconvergencerateandfastconvergencespeed,theBasicNewtonandModified Newtonmethodsareoftenusedtosolvetheoptimizationproblemsaccurately;however,thedisadvantagesarealsodemonstrable.Asit issimilartotheinversematrixreplacingHessianMatrixwithHesseMatrix,theQuasi-Newtonmethodproposedinthispaperis adopted to reduce the computational complexity; in the mean time, an objective function can be established by the changes in measuringthegradientineachiterationtoensurethesuperlinearconvergences,whichcontributestofreedomfromtheendlessloop. Afteralgorithmstepsarecomprehensivelyanalyzed,theclassicaltestfunctionisusedtotesttheapproximationeffectofQuasi-Newton methodinsolvingtheextremumofunconstrainedmultidimensionalfunction.

Key words: NewtonIterationmethod, multidimensionalfunctionextremum, ModifiedNewtonmethod, Quasi-Newtonmethod