| Most classic optimization algorithm based on Taylor mean value theorem, using the derivative information of the function at the iteration point, construct the polynomial approximation model to design.However,there are numerous real-world problems where derivatives are unavailable. So,derivative-free optimization methods become the best way to solve such problems, known as the direct method. It is very widely used in science and engineering calculation.Polynomial interpolation method is a derivative optimization algorithm, and its main idea is to use interpolation method to construct polynomial approximation model of the objective function, and it doesn’t need the derivative of information in the process of computing.This paper proposed two kinds of improved optimization algorithm based on the polynomial interpolation. One is applied the ideas of the conjugate gradient method to the interpolation algorithm to construct the search direction,the other is constructed the search direction according to the quasi-newton method. Compared with polynomial interpolation algorithm, the experimental results show good.Trust region method is the most common and effective method in solving nonlinear optimization problems.In the calculating,the selection of the trust region radius is an important factor to affect the effectiveness of the algorithm.In the traditional trust region method, we increase or decrease the radius in proportion according to the actual and forecast of the ratio of the objective function in each iteration, so the trust region radius is passive. In chapter 4, this paper proposes a new algorithm for the trust region algorithm, and the new algorithm combing the BB algorithm with the trust region algorithm,proposes a new strategy of automatically determining the trust region radius. Numerical results show that the algorithm is effective. |
