### A NEW NONMONOTONE TRUST REGION ALGORITHM FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

Jinghui Liu, Changfeng Ma

1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China
• Received:2011-12-14 Revised:2014-01-15 Online:2014-07-15 Published:2014-07-15
• Supported by:

This work has been partially supported by National Natural Science Foundation of China (11071041,11201074), Fujian Natural Science Foundation (2013J01006) and R&D of Key Instruments and Technologies for Deep Resources Prospecting (the National R&D Projects for Key Scientific Instruments) under grant number ZDYZ2012-1-02-04.

Jinghui Liu, Changfeng Ma. A NEW NONMONOTONE TRUST REGION ALGORITHM FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS[J]. Journal of Computational Mathematics, 2014, 32(4): 476-490.

Based on the nonmonotone line search technique proposed by Gu and Mo (Appl. Math. Comput. 55, (2008) pp. 2158-2172), a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

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