  Two-trust-region subproblem (TTRS), which is the minimization of a general
quadratic function over the intersection of two full-dimensional ellipsoids,
has been the subject of several recent research. In this paper, to solve TTRS,
a hybrid of efficient algorithms for finding global and local-nonglobal
minimizers of trust-region subproblem and the alternating direction method of
multipliers (ADMM) is proposed. The convergence of the ADMM steps to the first
order stationary condition is proved under certain conditions. On several
classes of test problems, we compare the new algorithm with the recent
algorithm of Sakaue et. al's \cite{SakaueNakat:16} and Snopt software.
