A New Hybrid Algorithm of Trust Region Methods

In the solution of trust region subproblem within the classical trust region algorithms, the centre of sphere is the current interaction point and one step-size is the upper bound. Considering that only with the negative gradient direction to acute angle may reduce the function value, we introduce the parameter to control of the centre of sphere and the radius. Based on the numerical experiments, obtains the value range of the parameter. The numerical evaluation demonstrates the validity of the new trust region algorithms.