The computation of the ground states of special multi-component 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 multi-component BECs. Second, the global convergent alternating Newton-Noda 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 "multi-block" optimization problems with spherical constraints. Numerical experiments are performed to evaluate the performance of proposed methods for different multi-component BECs, including pseudo spin-1/2, anti-ferromagnetic spin-1 and spin-2 BECs. These results support our theory and demonstrate the efficiency of our algorithms.

翻译：多组分玻色-爱因斯坦凝聚体（BECs）基态的计算可归结为具有球面约束的能量泛函极小化问题。经适当离散化后，该问题转化为非凸四次-二次优化问题。首先，我们将适用于单组分BECs的牛顿类方法推广至多组分BECs的交替极小化框架。其次，提出全局收敛的交替牛顿-野田迭代（ANNI）。特别地，我们证明了ANNI在温和条件下保持正性。最后，将分析应用于一类更一般的具有球面约束的"多模块"优化问题。通过数值实验评估所提方法在不同多组分BECs（包括赝自旋-1/2、反铁磁自旋-1及自旋-2 BECs）上的性能，结果验证了理论分析并展示了算法的高效性。