On the Convergence of Parallel Broyden Method

Abstract

Compare to the sequential Broyden method, an asynchronous parallel Broyden method is presented in the paper. We suppose that we have processors, which are divided into two groups. And the first group has processors, the second processors has processors, while the two groups are asynchronous parallel. If we assume that the objective function is twice continuously differentiable and uniformly convex, the global convergence of the algorithm is given. And under the same conditions, we show that the parallel Broyden method is superlinearly convergent.