Symmetric rank-one method based on some modified secant conditions for unconstrained optimization

The symmetric rank-one (SR1) method is one of the well-known quasi-Newton methods, and many researchers have studied the SR1 method. On the other hand, to accelerate quasi-Newton methods, some researchers have proposed variants of the secant condition. In this paper, we propose SR1 methods based on some modified secant conditions. We analyze local behaviors of the methods. In order to establish the global convergence of the methods, we apply the trust region method to our methods.