Nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization

作者：Zhao Lijuan; Sun Wenyu^*; de Sampaio Raimundo J B

来源：Frontiers of Mathematics in China, 2014, 9(5): 1211-1238.

DOI：10.1007/s11464-014-0356-8

• Nonmonotone technique
• conic model
• trust region method
• large scale optimization
• global convergence

We propose a nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional trust region methods, the subproblem in our method is a simple conic model, where the Hessian of the objective function is approximated by a scalar matrix. The trust region radius is adjusted with a new self-adaptive adjustment strategy which makes use of the information of the previous iteration and current iteration. The new method needs less memory and computational efforts. The global convergence and Q-superlinear convergence of the algorithm are established under the mild conditions. Numerical results on a series of standard test problems are reported to show that the new method is effective and attractive for large scale unconstrained optimization problems.

• 出版日期2014-10
• 单位南京师范大学