Abstract
This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modi- fied BFGS method is based on the new quasi-Newton equation Bk+1sk = yk where y k = yk + Aksk and Ak is a matrix. Wei, Li and Qi (WLQ) have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule. where g(x) denotes the gradient of f at x and k·kdenotes the Euclidean norm of a vector. We abbreviate g(xk), f(xk )a sgk, fk, respectively. The quasi-Newton algorithm is a practical method for solving unconstrained convex programme from the computation point of view. The convergence properties of the BFGS method for convex minimization have been studied by many researchers. There have already been a lot of achievements in global convergence properties of BFGS algorithm. Powell (2) has proved the global convergence properties of
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