中文摘要：

The trust region(TR) method for optimization is a class of effective methods.The conic model can be regarded as a generalized quadratic model and it possesses the good convergence properties of the quadratic model near the minimizer.The Barzilai and Borwein(BB) gradient method is also an effective method,it can be used for solving large scale optimization problems to avoid the expensive computation and storage of matrices.In addition,the BB stepsize is easy to determine without large computational efforts.In this paper,based on the conic trust region framework,we employ the generalized BB stepsize,and propose a new nonmonotone adaptive trust region method based on simple conic model for large scale unconstrained optimization.Unlike traditional conic model,the Hessian approximation is an scalar matrix based on the generalized BB stepsize,which resulting a simple conic model.By adding the nonmonotone technique and adaptive technique to the simple conic model,the new method needs less storage location and converges faster.The global convergence of the algorithm is established under certain conditions.Numerical results indicate that the new method is effective and attractive for large scale unconstrained optimization problems.

英文摘要：

The trust region （TR） method for optimization is a class of effective methods. The conic model can be regarded as a generalized quadratic model and it possesses the good convergence properties of the quadratic model near the minimizer. The Barzilai and Borwein （BB） gradient method is also an effective method, it can be used for solving large scale optimization problems to avoid the expen- sive computation and storage of matrices. In addition, the BB stepsize is easy to determine without large computational efforts. In this paper, based on the conic trust region framework, we employ the generalized BB stepsize, and propose a new nonmonotone adaptive trust region method based on simple conic model for large scale unconstrained optimization. Unlike traditional conic model, the Hessian approximation is an scalar matrix based on the generalized BB stepsize, which resulting a simple conic model. By adding the nonmonotone technique and adaptive technique to the simple conic model, the new method needs less storage location and converges faster. The global convergence of the algorithm is established under certain conditions. Numerical results indicate that the new method is effective and attractive for large scale unconstrained optimization problems.