交替方向乘子法解对称特征值互补问题

Alternating direction method of multipliers for symmetric eigenvalue complementarity problems

将对称特征值互补问题等价转化为单纯形约束的瑞利商极大化问题,提出一种交替方向乘子法。通过引入辅助变量,将单纯形约束进行分离,避免了单纯形集合投影无封闭解的缺陷。数值实验结果表明,与经典的谱投影梯度算法相比,在求解较大规模问题时,提出的方法需要更少的计算时间。

The symmetric eigenvalue complementarity problem is equivalent to the problem of maximizing the Rayleigh quotient with simplex constraints,and the alternating direction method of multipliers is proposed.By introducing instrumental variables,the simplex constraint is separated to avoid the defect that the projection of the simplex set has no closed solution.Compared with the classical spectral projection gradient algorithm,the numerical results show that the proposed method takes less computing time for solving large scale problems.