Abstract: Trust region algorithm is an important numerical method to solve unconstrained optimization problems at present， and the solution of trust region subproblem is the key to realizing the trust region algorithm. In this paper， three methods for solving trust region subproblems（indeterminate broken line method， Moré-Sorensen method and truncated conjugate gradient method） are described. A large number of numerical tests are carried out on the above three methods by using the unconstrained optimization test function package widely used in the world. The results show that to some extent， the efficiency of the truncated conjugate gradient method is better than the other two methods， and the non-monotone trust region algorithm is better than the traditional monotone algorithm to some extent.

Key words: trust region algorithm, trust region subproblem, numerical efficiency, Matlab