Research On Line Search Methods And Trust Region Methods In Unconstrained Optimization

Line search methods and trust region methods are important technologies to ensure global convergence in optimization algorithms. Their common purpose is to compute the displacement at each iteration step in any optimization algorithms and obtain a new iteration point. But the methods of produce iterative step are different. Line search methods first create the direction of displacement (also known as search direction), and then determine the stepsize of displacement, while the trust region methods directly determine the displacement.This paper focuses on line search methods and trust region methods. First, we propose two improved methods of the golden section method, named LU golden section method and Biparabola method. By theoretical and numerical analysis, the two proposed methods have better convergence speed than the classic golden section method. Then, we analyze several improved methods of classical trust region methods, particularly the combination of trust region methods and line search methods, we implement the function and the experimental results have shown that the combination of the traditional trust region methods and the BFGS quasi-Newton method. For the combination of trust region methods and line search methods, at the end of article, we propose the combined method of the trust region methods and the improved method of golden section method, and analyze the advantages of such combined algorithm.