中文摘要：

为了求解大型矩阵方程的多约束优化问题,基于Dykstra交替投影算法和相关的矩阵分解理论,提出了求解矩阵方程AXA^T=B的多约束条件下的最小二乘解的迭代算法,并讨论了算法的收敛性。数值实验验证了算法的有效性。

英文摘要：

In order to solve the multiple constrained optimization problem of the large-scale matrix equation,based on Dyk-stra’s alternating proj ection algorithm and the relevant matrix decomposition theory,an iteration algorithm is proposed to solve the multiple constrained matrix equation least squares solution.The convergence properties of the algorithm are dis-cussed,and the numerical experiments show that the algorithm is effective.