Author(s)

Yang Zhang¹, Quanming Ji¹, Qinghua Zhou^1,2*

¹College of Mathematics & Information Science, Hebei University, Baoding, China.
²School of Applied Mathematics, Beijing Normal University, Zhuhai, China.

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.

Unconstrained Optimization, Trust Region Method, Nonmonotone Technique, Global Convergence, Superlinear Convergence

Zhang, Y. , Ji, Q. and Zhou, Q. (2021) A New Nonmonotone Adaptive Trust Region Method. Journal of Applied Mathematics and Physics, 9, 3102-3114. doi: 10.4236/jamp.2021.912202.