Nonmonotonic Trust Region Algorithms For Unconstrained And Constrained Optimization

In this paper, nonmonotonic trust region algorithms for unconstrained and constrained optimization are discussed. The paper is divided into three parts, the contents are following:In the first chapter, nonmonotonic trust region methods for unconstrained optimization are discussed. Trust region method is simply introduced in the first part; in the second pait, the basic trust region algorithm is given; A new nonmonotonic trust region method and Us convergence are given in the third pan: in the fourth part, a nonmonotonic trust region method for unconstrained multiobjective programming is discussed, and its convergence is proved.In the second chapter, nonmonotonic trust region algorithms for linear constrained optimization are discussed. In the first part, progress in the field are introduced; Absorbing the idea of the reference [29], a nonmonotonic trust region method with linesearch for linearly constrained optimization is given and its convergence is proved.In the third chapter, nonmonotonic trust region algorithms for nonlinear constrained optimization are discussed. In the first pan, progress in the field are given; in the second part, a class of nonmonotonic trust region methods for nonlinearly constrained optimization is discussed and its convergence is given.