A hybrid algorithm for the two-trust-region subproblem

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 test problems, we compare the new algorithm against three competitors: the Snopt software, the algorithm proposed by Sakaue et al. (SIAM J Optim 26:1669–1694, 2016 ) and the CADMM algorithm proposed by Huang and Sidiropoulos (IEEE Trans Signal Process 64:5297–5310, 2016 ). The numerical results show that the new algorithm is competitive.