凸多面体上垂直线性互补问题的二次收敛算法  

A Quadratically Convergent Algorithm for the Vector Linear Complementarity Problem over a Convex Polyhedron

作　　者：凌思涛[1] 刘为竹[2] 魏玉帅 

机构地区：[1]曲阜师范大学运筹与管理学院,山东日照276826 [2]临沂师范学院附中,山东临沂276005 [3]临沂二中,山东临沂276000

出　　处：《临沂师范学院学报》2007年第3期19-23,共5页Journal of Linyi Teachers' College

摘　　要：借助Fischer函数将凸多面体上的垂直线性互补问题(VLCP)等价地转化为一个非线性方程组系统,在较弱条件下,给出了VLCP的误差界;同时,给出了一种求解VLCP的Levenberg-Marquardt方法,并在不要求存在非退化解的条件下证明了这种方法的全局收敛性和二次收敛性.In this paper, by using the Fischer function, the vector linear complementarity problem over a convex polyhedron（VLCP） is equivalently reformulated as a system of nonlinear equations, and we give error bound for VLCP under relatively weaker conditions. At the same time, the famous Levenberg-Marquardt algorithm is given for obtaining its solution. It is showed that this algorithm is both globally and quadratically convergent without nondegenerate solution.

关 键 词：垂直线性互补问题 误差界 二次收敛 

分 类 号：O242[理学—计算数学]