| In this paper,polynomial interpolation is used to approximate unconstrained optimization problems.In general unconstrained optimization problems,some relatively simple functions are usually used to approximate the objective function locally due to the complexity of the objective function calculation,and then an iterative algorithm is constructed.In this paper,we use the simple form of the first-order polynomial function,the quadratic polynomial function without cross terms and the complete quadratic polynomial function to approximate the original function.This method greatly reduces the complexity of calculation and improves the efficiency of calculation,and then becomes one of the many optimization methods that many scholars highly respect.In the first chapter,some classical algorithms for solving unconstrained optimization problems are introduced.In the second chapter,the interpolation method is combined with the classical quasi Newton method and trust region method.Based on the idea of improving trust region radius and trust region center,especially,the interpolation trust region method is improved.Finally,BFGS correction is added to the algorithm.The third chapter is about two special tests of optimization problems.One is the idea of"large scale" in global optimization.Based on a variety of test functions,the paper explores the influence of the size of interpolation node coverage area of approximation model on the convergence efficiency of the algorithm.The second is to analyze the impact of the setting of the near zero point of the optimal solution of the test function on the convergence test efficiency of the algorithm,mainly to explore the impact of the rounding error of the programming software on the performance of the algorithm. |
