求解实对称互补特征值问题的积极集方法

Active Set Method for Solving Real Symmetric Complementary Eigenvalue Problem

摘要:

基于序列二次规划算法构造了求解实对称互补特征值问题的一类积极集方法。 通过特殊的积极集指标选取策略，该积极集方法计算得到的迭代序列具有单调下降特征，并从理论上证明了该方法的收敛性。 数值实验结果表明该方法是行之有效的，并且在互补性和迭代时间上均优于Matlab软件的内置算法。

Abstract:

Based on the sequential quadratic programming algorithm， a class of active set methods for solving real symmetric complementary eigenvalue problems is constructed in this paper. By designing a special strategy with the active set index selection， the iterative sequence generated by the active set method has the characteristics of monotonous decline， and the convergence of the method is theoretically proved. The numerical experimental results show that the method is effective and superior to built-in algorithm of MATLAB in complementarity and iteration time.