A Self-Adaptive Trust Region Algorithm with Line Search Technique

In this paper, we propose an algorithm for unconstrained optimization that employs both adaptive trust region techniques with line searchs. Unlike traditional adaptive trust region methods, our algorithm does not resolve the sub problem if the trial step isn't accepted, but instead performs the Wolfe line search at each iteration. Under mild conditions, the global convergence is proved and the super linear convergence of the new algorithm is shown without the condition that the Hessian of the objective function at the solution be positive definite. Preliminary numerical results indicate that the performance of the new method is very efficient.