Global Convergence of Quasi-Newton Methods for Solving Nonconvex Minimization Problems

摘要

In this paper, we consider a class of modified Broyden methods for solving unconstrained optimization problems. Since the Hessian matrix of objective function is generally not positive definite when the objective function is nonconvex, it would be reasonable to expect that a proper modification of the Broyden methods is effective for nonconvex problems. Based on this view, we give a new secant equation for the methods, and present a calss of modified Broyden methods. Furthermore, if we assume that the line search satisfies a standard sufficient decrease condition, we establish global convergence of the methods.