In this paper we develop a new trust region method with adaptive radius for unconstrained
optimization problems. The new method can adjust the trust region radius automatically at
each iteration and possibly reduces the number of solving subproblems. We investigate the
global convergence and convergence rate of this new method under some mild conditions.
Theoretical analysis and numerical results show that the new adaptive trust region radius is
available and reasonable and the resultant trust region method is efficient in solving …

In this paper, we propose a new adaptive trust region method for unconstrained optimization
problems. In the new method, we use the previous and the current iterative information and
a new update rule to define the trust region radius at each iterate. The global and
superlinear convergence properties of the method are established under reasonable
assumptions. Preliminary numerical results show that the new method is efficient and
attractive for unconstrained optimization problems.