The Application of a Modified Algorithm on Quadratic Interpolation Models

In this paper, we propose a modified method on quadratic interpolation models which are updated by Frobenius norm. The method uses the progressively obtained information during the iterations of the algorithm to form new search subspaces. Then the quadratic model is solved in the new subspaces. The main idea is to use the information revealed in the previous steps to construct more promising directions. The effectiveness is proved in that the numbers of function evaluations are reduced obviously for most testing problems. At the end of this paper, we tested the algorithm on some variable dimension problems.