NEWTON-BASED ALTERNATING METHODS FOR THE GROUND STATE OF A CLASS OF MULTICOMPONENT BOSE--EINSTEIN CONDENSATES

The computation of the ground state of special multicomponent Bose--Einstein condensates (BECs) can be formulated as an energy functional minimization problem with spherical constraints. It leads to a nonconvex quartic-quadratic optimization problem after suitable discretizations. First, we generalize the Newton-based methods for single-component BECs to the alternating minimization scheme for multicomponent BECs. Second, the global convergent alternating NewtonNoda iteration (ANNI) is proposed. In particular, we prove the positivity preserving property of ANNI under mild conditions. Finally, our analysis is applied to a class of more general ``multiblock"" optimization problems with spherical constraints. Numerical experiments are performed to evaluate the performance of proposed methods for different multicomponent BECs, including pseudo spin-1/2, antiferromagnetic spin-1 and spin-2 BECs. These results support our theory and demonstrate the efficiency of our algorithms.