Abstract: According to the sequential BFGS method,in this paper we present an asynchronous parallel BFGS method in the case when the gradient information about the function is inexact.We assume that we have p+q processors, which are divided into two groups,the first group has p processors,the second group has q processors,the two groups are asynchronous parallel.If we assume the objective function is twice continuously differentiable and uniformly convex,we prove the iteration converge globally to the solution,and under some additional conditions we show the method is superlinearly convergent.Finally,we show the numerical results of this algorithm.

Key words: BFGS algorithm, superlinear convergence, parallel method