【作者】 杨超；

【导师】 杨卫红；

【作者基本信息】 复旦大学 ， 计算数学， 2013， 硕士

【摘要】 二阶锥互补问题(SOCCP)是在实际应用中广泛出现的一类问题,熟知的线性互补问题(LCP)则是它的一种特殊情形.本文的目的是给出了一种基于矩阵分裂思想的求解对称的SOCCP的迭代方法.最初矩阵分裂法的提出是用来求解线性方程组,并随后被推广至用于求解先行互补问题(LCP)以及仿射变分不等式问题.在本文中,我们首先给出了矩阵分裂法的基本框架及其收敛性的条件分析,然后作为矩阵分裂法的一个特别应用,对二阶锥互补问题给出给出了块的逐次超松弛法(BSOR),并对其子问题给出有效的求解方法以及相关的数值实验结果.最后,作为SOCCP的矩阵分裂方法的一个应用,我们考虑了二阶锥规划(SOCP)问题,给出了一个基于线搜索法的求解算法及相关的数值结果.更多还原

【Abstract】 The second order cone complementarity problem(SOCCP) is a wide range class of problems that contains the linear complementarity problem(LCP) as a special case. The purpose of this paper is to propose an iterative method for the symmetric SOCCP that is based on the idea of matrix splitting. Matrix splitting methods have originally been developed for the solution of the system of linear equations and that subsequently been extended to the LCP and the affine variational inequality problem. In this paper, we first give the framework of matrix splitting method and its convergence analysis, we then present, as a particular realization of the matrix-splitting method, the block succes-sive overrelaxation(SOR) method for the SOCCP, and propose an efficient method for solving subproblems, then report some numerical results with the proposed algorithm. Finally, as an application to the matrix-splitting method for SOCCP, we consider the second-order cone programming(SOCP) problem, and then give an algorithm based on line search method plus some related numerical results.更多还原