Abstract
In this paper, a modification of the BFGS algorithm for unconstrained nonconvex optimization is proposed. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation Bk+1sk=yk*, where yk* is the sum of yk and tk‖g(xk)‖sk. The global convergence property of the algorithm associated with the general line search rule is prove.
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