A New Nonmonotone BB-TR Method Based On Simple Conic Model For Large Scale Unconstrained Optimization

In this paper, we study a BB-TR method based on simple conic model for solving large scale unconstrained optimization problems.There are many trust region methods for unconstrained optimization and the trust region method based on conic model is an effective one. The conic model can be re-garded as a generalized quadratic model and contains more information of the objec-tive function. What’s more, the conic model is equal to a quadratic model when the iterate is close to the minimizer. That is to say, the conic model retains the quadratic model’s good convergence properties near the minimizer. For the good performance of the conic trust region method, it has attracted the attention of many experts and scholars in the last ten years. The Barzilai and Borwein gradient method is an effec-tive method. And it can be used for solving large scale optimization problems, for avoiding the computation and storage of some matrices. In addition, the BB stepsize is easy to determine without complex computation.We combine the conic trust region method with the Barzilai and Borwein gradi-ent method, and propose a new nonmonotone adaptive trust region method based on simple conic model for unconstrained optimization. Unlike traditional conic model, the Hessian approximation is an scalar matrix based on the BB stepsize, which re-sulting 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 and superlinear convergence results are es-tablished under certain conditions. Numerical results indicate that the new method is effective and attractive for large scale unconstrained optimization problems.