解线性互补问题的并行交替迭代算法

PARALLEL ALTERNATING ITERATIVE ALGORITHM FOR LINEAR COMPLEMENTARITY PROBLEM

运用交替迭代算法与并行计算,提出了求解线性互补问题的并行交替迭代算法.当矩阵的多重分裂分别为第一类弱正则多重分裂、第二类弱正则多重分裂以及P-正则多重分裂时证明了算法的全局收敛性.该算法具有计算量小、计算速度快、并行计算等特点,因而特别适于求解大规模问题.数值结果表明,该算法是十分有效的.

By combining Alternating Iterative Algorithm and Parallel Multi-splitting, the authors first set up Parallel Alternating Iterative Algorithm for solving the linear complementarity problem. It is shown that when the multisplittings of matrix are weak nonnegative of the first type or the second type, both models lead to convergent schemes. And then, when the multisplittings are P-regular, they establish the global convergence theory of the algorithm. The algorithm has less computational complexity and quicker velocity and is especially suit- able for parallel computation of large-scale problem. The numerical experiments show the efficiency of the algorithm.