A Self-Adaptive Filter Trust Region Method For Unconstrained Optimization

In the traditional trust region whenρk>η1 we accept the new point x+k=xk+dk, trust region method join filter technology can increase the risk of try point x+k accepted. For the choice of the trust region radius, the trust region radius of traditional trust region are blindness for it radius are artificial zoom in or out. The choice of trust region radius nothing to do with gk and Hk, but trust region sub-problems has close relation with gk and Hk. Obviously, it is inappropriate for the traditional trust region radius update. In this paper, the trust region radius update using self-adaptive selection method, so that the update of the trust region radius is more suitable for algorithm itself.There are three chapters in this paper. In chapter one, we introduce the traditional trust region, the basic concept of filter algorithms and its ideas, the strategy of trust region radius adjustment and the work that this thesis has done. In chapter two algorithm2.1, we combine the self-adaptive selection method with the filter trust region method for unconstrained optimization. Not only increase the accepted chance of point x+k, but make the update of trust region radius more suitable for algorithm itself. Algorithm2.2, on the basis of method presented in algorithm2.1,a new self adaptive filter trust region method with line search technique is proposed. Reduce the number of resolving sub-problem, make the test point x+k is likely to filter to accept to the largest.Finally, we proved the convergence of the algorithm.Compared algorithm2.1 with traditional trust region method, filter trust region method and self-adaptive trust region method, numerical experiment show that algorithm 2.1 is effective. Compared algorithm 2.2 with algorithm 2.1, numerical results show the effectiveness of adding line search technique. In front of all are monotonous trust region, but for some practical problems monotonic decline can not ensure effectiveness. Therefore, in chapter three, we introduce non-monotone line search technique, In the iterative process, allowing objective function value nonmonotonic. At the same time, improved the test point's acceptance conditions, made the actual reduction function in correspronding with predicted reduction function.