A Class Of New Non-monotone Trust Region Methods

Trust region method plays an important role in solving the optimization problem,and it is one of the most effective algorithms for solving nonlinear optimization problems.While,non-monotone techniques have unique advantages in solving non-quadratic problems and avoiding Martos effects.In this work,we study a new class of non-monotone trust region method.For the trust region algorithms of unconstrained optimization problem,one of the most important is how to solve the sub-problem.It is well known that when the search direction and the negative gradient direction are obtuse angles,the objective function value does not decrease.And only when the search direction and the negative gradient direction are acute angles,the objective function value decreases.The solving process of the traditional sub-problem does not consider this part of the factors which will affect the algorithm's convergence rate.Based on this,we propose an improved non-monotone trust region sub-problem model.In this work,a new sub-problem construction of trust region algorithms is adopted,and some popular non-monotone forms are applied to the improved trust region algorithm.This work is divided into four chapters.Here are the details:In the first chapter,the research background,research status and the development of trust region algorithm are discussed in detail.The second chapter introduces the traditional trust region and the new sub-problem model of the new trust region algorithm,as well as several popular non-monotone techniques.In the third chapter,we combine the improved new trust region algorithm with the three popular non-monotone techniques.The main processes of the algorithms are described in detail,and the convergences theories of these improved algorithms are theoretically analyzed.Also we prove the effectiveness of the algorithm by numerical experiments.In the last chapter,the new non-monotone trust region methods proposed in this work are summarized and forecasted.