The Convex Function Of Broyden Algorithm Research

In this paper, we study global convergence properties of Broyden class of quasi-Newton methods, when applied to non-convex functions. First we state some fundamen-tal properties of quasi-Newton methods, especially Broyden class. Then we focus on the convergence property of this method when applied to non-convex functions. In this part we originally give a condition and prove that in this condition the methods of Broyden class ((?)≠1) can converge globally when applied to non-convex function. Under certain conditions, we also establish superlinear convergence of this class of methods. Next, we consider a well-known condition that has already been the sufficient condition of conver-gence of BFGS method. We prove that this condition can also be the sufficient condition of convergence of Broyden class{(?≠1) of methods. Finally we show some numerical examples of this class of methods. The results show that Broyden class of methods are adaptive to non-convex functions.