Non-Monotone Trust Region Algorithms For Unconstrained And Constrained Optimization

In this work, we discuss some non-monotone trust region algorithms for unconstrained and constrained optimization. The contents are as follows:In the first chapter, the research background and significance of this work are introduced.Then, we discuss the non-monotone trust region algorithm for unconstrained optimization in the second chapter. Firstly, a new non-monotone Wolfe line search algorithm is given, and its convergence is proved. Furthermore, we propose a new family of non-monotone trust region algorithm by combining the new algorithm above with non-monotone trust region method and self-adaptive technique. There are several advantages of our algorithm, one of them is that the algorithm solves the trust region sub-problem only once at each iteration, the other is that the matrix approximation to the Hessian simultaneously satisfies the quasi-Newton condition and maintains its positive definiteness, also the new algorithm using self-adaptive technique avoids the blindness of choosing trust region radius. Besides, the convergence property of the algorithm is proved at the end of the second chapter.In the third chapter, non-monotone trust region methods for equality constrained optimization are discussed. Through analyzing current development in this field, according to different trust region sub-problems, we discuss two kind of non-monotone trust region algorithms for equality constrained optimization and analysis their convergence.Finally, in the fourth chapter we summarize the main work of this paper and prospect some future work.