A conic regularized Barzilai-Borwein trust region method for large scale unconstrained optimization

In this paper, we propose a conic regularized Barzilai-Borwein trust region method for large scale unconstrained optimization. Different from traditional trust region method, the subproblem in new method is a simple conic model, whose approximate Hessian is replaced by a regularized Barzilai-Borwein step. Unlike traditional trust region method, when trial point is not accepted by trust region, line search technique is used to find an acceptable trial point, rather than resolving trust region subproblem. Global convergence is described under some mild conditions. Compared to Barzilai-Borwein method based on simple conic model and the one based on simple quadratic model, our new method requires less storage requirement and less computational complexity. The new method is tested on a series of standard large scale CUTEr testing problems, numerical results are reported to show that new method is effective and attractive.