In this paper a new trust region method with simple model for solving large-scale unconstrained nonlinear optimization problems is proposed. By using the generalized weak quasi-Newton equations, we derive several schemes to determine the appropriate scalar matrix as the Hessian approximation. Under some reasonable conditions and the framework of the trust-region method, the global convergence of the proposed algorithm is established. The numerical results and comparison on 56 test functions with dimensions from 50 to 20000 in CUTEr collection indicate that the new method is efficient and competitive.
Report No. opt-2015-3-5. School of Mathematical Sciences, Nanjing Normal University, Nanjing, China.