Several New Algorithms For Unconstrained Optimization Problems

For the unconstrained optimization problem,the trust region algorithm is one kind of main methods.In the traditional trust region algorithm,the selection of the trust region radius is often based on the previous experience that has been determined,so there is some kind of blindness.In order to solve the above defects,adaptive technology and retrospective technology are proposed.In this paper,a non-monotonic strategy is added to the proposed algorithms on the basis of retrospective technology and adaptive technology to solve the unconstrained optimization problems.The algorithms enjoy the global convergence under some mild conditions.The main work of this paper has the following aspects:Firstly,this paper applies adaptive technology and non-monotonic technology to trust region method,proposes non-monotonic adaptive trust region algorithm,and studies the properties of the algorithm.Secondly,based on the retrospective adaptive trust region algorithm,this paper introduces the non-monotonic term T_k and defines two new non-monotone ratio r_k+1^NR and r_k^NB,thus proposes a new algorithm for solving unconstrained optimization problems.Global convergence is proved too.Finally,this paper adds the non-monotonic term f_l?k?to the retrospective adaptive cubic regularization algorithm,and also its convergence is proved.