## Solving unconstrained discrete-time optimal control problems using trust region method |

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Advanced Computing Research AfBne Scaling Method Aiping Liao Algorithm I Algorithm Algorithm subP Applying Algorithm g assume that H C-L Algorithm calculating the Newton Coleman and Liao Coleman and Wei Computing Research Institute convergence property Cornell Theory Center corresponding trust region discrete-time optimal control eigenvector explicit form f(xk Fadil Santosa find an approximate finite many iterations Gay's H is positive H~lg Hessian identity matrix indexi inverse power method Iter Iter(Feva iteration of Algorithm LH(yH Liao 13 limit point line searches method for solving Newton direction Nocedal-Yuan algorithm number of operations Numerical results Pantoja's procedure positive semidefinite Proof Proposition 2.2 pure trust region Region Method Aiping results for problem satisfies set Ak+i set x*+1 solution to subP Solve subP solving the trust Sorensen 17 step Theorem 2.1 total number trust region algorithms trust region method trust region subproblem unconstrained discrete-time optimal update vector Wei Yuan XI is positive xk+1 Yuying