Improved trust region method for quadratic interpolation models

An improved method is used to solve unconstrained optimization problems,when the derivatives of the objective function can not be available or the calculation of the derivatives are too expensive.Generally speaking,the objective function is approximated to quadratic interpolation model which is solved in a traditional trust region.The traditional trust region method is improved in this paper,and formed two novel trust region subproblems.The innovation of the improved trust region algorithm is that it solving the quadratic interpolation model in one parameterized trust region and modifying the model in another parameterized region,which can save the calculation and improve the accuracy.The improved trust region method can quickly find a descent direction and a poised interpolation point in two improved trust regions,respectively.Experimental results reveal that the improved method is more effective than the classic trust region method on the testing problems.