EAOR投影迭代算法求解一类对称双正型线性互补问题

EAOR Projective Iterative Algorithm for Solving Symmetric and Copositive Linear Complementarity Problems

研究求解一类对称双正型的线性互补问题的EAOR迭代算法.证明了由此算法产生的迭代序列的聚点是线性互补问题的解.并且,当互补问题中的矩阵为对称双正加阵或严格对称双正阵时,算法产生的迭代序列存在子序列收敛到互补问题的解.而当矩阵为非退化对称双正加阵时,该序列收敛.

The EAOR algorithm for solving symmetric and copositive linear complementarity problems was studied. It is shown that any accumulation point of the iteration generated by the algorithm solves the linear complementarity problem. When the matrix A involed in the linear complementarity problem is a symmetric and copositive plus matrix or a symmtric and strictly copositive matrix, the sequence generated by the algorithm exists an accumulation, which solves the linear complementarity problem. Moreover, when A is a nondegenerate,symmetric and copositive plus matrix, the sequence converges to a solution of the problem.