A New Nonmonotone Adaptive Trust Region Method  

作　　者：Yang Zhang Quanming Ji Qinghua Zhou Yang Zhang;Quanming Ji;Qinghua Zhou(College of Mathematics & Information Science, Hebei University, Baoding, China;School of Applied Mathematics, Beijing Normal University, Zhuhai, China)

机构地区：[1]College of Mathematics & Information Science, Hebei University, Baoding, China [2]School of Applied Mathematics, Beijing Normal University, Zhuhai, China

出　　处：《Journal of Applied Mathematics and Physics》2021年第12期3102-3114,共13页应用数学与应用物理（英文）

摘　　要：The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.The trust region method plays an important role in solving optimization problems. In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems. Actually, we combine a popular nonmonotone technique with an adaptive trust region algorithm. The new ratio to adjusting the next trust region radius is different from the ratio in the traditional trust region methods. Under some appropriate conditions, we show that the new algorithm has good global convergence and superlinear convergence.

关 键 词：Unconstrained Optimization Trust Region Method Nonmonotone Technique Global Convergence Superlinear Convergence 

分 类 号：O22[理学—运筹学与控制论]