A trust-region method with two subproblems and backtracking line search for solving unconstrained optimization is proposed. At every iteration, we use the truncated conjugate gradient method or its variation to solve one of the two subproblems approximately. Backtracking line search is carried out when the trust-region trail step fails. We show that this method have the same convergence properties as the traditional trust-region method based on the truncated conjugate gradient method. Numerical results show that this method is as reliable as the traditional one and more efficient in respect of iterations, CPU time and evaluations. Mathematical subject classification: Primary: 65K05; Secondary: 90C30.
truncated conjugate gradient; trust-region; two subproblems; backtracking; convergence
