New choices of search directions used in constructing quadratic interpolation models

In this paper, some quadratic interpolation models are constructed by developing new trust region sub-problems. These sub-problems are derived by modifying search directions which combine the information progressively obtained during the iterations of the algorithm to form new search subspaces. The quadratic models are solved in the new subspaces. The motive is to use the information disclosed by the previous steps to construct probably more promising directions. The effectiveness is proved in that the number of function evaluations are reduced obviously for most tested problems. At the end of this paper, we test the models on some variable dimension problems.