中文摘要：

为求解不相容矩阵不等式AXB ＋CYD ≥E 的对称解，给出矩阵不等式有解的充分必要条件。提出了一种迭代算法，该算法以谱投影梯度法为主要框架。在适当条件下证明了算法的收敛性。

英文摘要：

Aiming at the symmetric solution of the inconsistent matrix inequalityAXB＋CYD ≥E ,the sufficient and necessary conditions for the matrix inequality existing solution are derived.An iteration method is proposed.This method uses spec-tral projected gradient method （SPG）as the primary frame.The convergence of the given algorithm under certain conditions is proved.