On the branch and bound algorithm for the extended trust-region subproblem

In this paper, by an example we show a defect of the Branch and Bound (BB) algorithm of Beck & Pan (J Glob Optim 69:309–342, 2017) for solving the extended trust-region subproblem ( m -eTRS) when the trust-region subproblem (TRS) is hard case 2. Then, to resolve the defect, we propose to solve a subproblem at the root node in order to check whether TRS in the hard case 2 has an optimal that is also feasible and thus optimal for m -eTRS. On several randomly generated test problems, we show that the enhanced algorithm is significantly better than the original BB algorithm in terms of CPU times and fathomed nodes.