On Adaptive Trust-Region Methods For Unconstrained Optimization Problems

Trust region method is a kind of efficient and robust method to solve general unconstrained optimization. And the choice of the trust region radius is very important to the efficiency of the method. Recently Zhang et. al. [1] proposed a new trust region method called adaptive trust region method, in which the trust region radius depends on the gradient and Hessian of the current iterate point. Numerical results show the efficiency of the method. The first part of this thesis combines the nonmonotone technique to the adaptive trust region method. The global and superlinear convergence results of the algorithm are established. Numerical results show that the nonmonotone method is more efficient. The second part of this thesis puts the adaptive technique to the conic trust region method, and we also give the global and superlinear convergence results of the new method. Numerical results show that the new method is efficient.