A Modified Adaptive Conic Trust Region Algorithm

In this paper, we combine the adaptive conic trust region method with the quasi-Newton line search method, and then propose a new modified adaptive conic trust region algorithm which solves unconstrained optimization problems. The new algorithm not only retains the desirable global convergence of trust region methods and the local super-linear convergence of quasi-Newton methods, but also overcomes their drawbacks at the same time. Global convergence and local super-linear convergence of the new algorithm are proved. The initial numerical experiments show that the new algorithm is efficient.