BFGS Parallel Algorithm of Unconstrained Optimization Problems and Its Implementation

Based on analysis of both the Broyden-Fletcher-Goldfarb-Shanno(BFGS) algorithm and its convergence properties of unconstrained optimization problems,this paper presents a parallel algorithms of BFGS by using the row interleaved format parallel decomposition of Cholesky,the synchronous parallel Wolfe-Powell non-linear search and the modified formula of BFGS.The paper also analyszs the time complexity and speedup ratio of the algorithm.Experimental results of PC cluster show that the BFGS parallel algorithm improves solution speed of unconstrained optimization problems.The theoretical analysis and the experimental results of BFGS parallel algorithm are consistency with a linear speedup ratio.