On the use of hybrid models in wedge trust region

In this paper, we have constructed a new algorithm for unconstrained optimizations based on the wedge trust region method. It is designed for solving problems in which the gradient of the object function is not available and the number of variables is moderate. After reviewing the separate contributions of the linear models and the quadratic models, here we propose a hybrid model to update the wedge trust region radius. Comparison of the new algorithm with both version of interpolation methods are reported in this paper. Numerical results show the applicability of our new algorithm to practical problems.