Reseach Of Conjugate Gradient Methods For Unconstrained Optimization

This paper researches conjugate gradient methods for unconstrained optimiza -tion.Conjugate gradient methods are widely used for unconstrained optimization, especially for solving large-scale unconstrained problems.In the first two chapters,wesum up the background and significance and the present situation of conjugate gradient methods through extensive reading and research. Furthermore,we present basic knowledge for studying conjugate gradient methods.Conjugate gradient methods are still worth researching though many scholars have done lots of work about them. Using Hybrid Strategy is a excellent method to study conjugate gradient methods for making the best use of the convergence and the good numerical performance.In chapter 3 and 4,we present two new hybird gradient methods on the basis of good convergence ofDYmethod.Furthermore,we prove the decent property and globle convergence of the new methods.In general,we will pay attention to two questions when reseaching unconstrained optimization: search direction and search condition.In last chapter,we present a new search condition on the basis of Wolfe line search and prove the decent property and globle convergence of the new methods.The numerical results illustrate that the new methods are effective whether the improvement of search direction or earch condition.