Some Researchs And Improvements On Non-monotone Trust Region Algorithm With A Line Search

This paper studies the trust region algorithms combined with inexact line search technique for solving unconstrained optimization problems,the main content of the thesis is presented as follows:In Chapter 2,Based on the traditional rules of inexact Armijo line search,a new kind of Armijo line search rule was established.At the same time,combining the trust region algorithm and using the sparse diagonal quasi-newton technology can effectively solve the unconstrained optimization problems.Under some reasonable conditions,we analyses the convergence of the new algorithm,and prove the feasibility of the new algorithm through the numerical experiments.In Chapter 3,We first explores a new non-monotone Wolfe line search technique,and then apply it to the traditional trust region algorithm with line search.The difference is that the rules of the new Wolfe line search is used in each iteration of the new algorithm in order to obtain the next iteration point,so the advantage of this is that they can ensure the positive definite transitivity of the iterative matrix.Then under the right circumstances,we proved the global convergence of the algorithm.Finally,we verify the effectiveness of the new algorithm through different numerical examples.In Chapter 4,we improve the existing rules of the large-step Armijo line search.Based on the Zhang H.C.non-monotone rule,a new kind of non-monotone trust region algorithm with non-monotone line search is proposed,and under certain assumptions,the global convergence of the algorithm are analyzed and proved.Numerical experiments show that this new algorithm indeed has significant advantages in the calculation process,especially for the large-scale problems.