一种求解线性圆锥互补问题的非精确光滑牛顿法  

An inexact smoothing Newton method for linear circular cone complementarity problems

作　　者：韦洪锦 迟晓妮[2] 黄鸿柳 李春红 WEI Hongjin;CHI Xiaoni;HUANG Hongliu;LI Chunhong(School of Mathematics and Computer Science,Guangxi Science&Technology Normal University,Laibin 546100,China;School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]广西科技师范学院数学与计算机科学学院,广西来宾546100 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2021年第3期230-235,共6页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11861026);广西自动检测技术与仪器重点实验室基金(YQ18112);广西高校中青年教师科研基础能力提升计划(2019KY0866,2019KY0868,2019KY0854)。

摘　　要：在标准内积下,圆锥通常是非对称锥,这给圆锥互补问题的算法研究带来了巨大的挑战,因此如何找到好的算法求解圆锥互补问题是一个热点问题。在光滑牛顿法框架下,给出一种求解线性圆锥互补问题的非精确光滑牛顿法。该算法先运用一个新的圆锥互补函数的光滑函数将圆锥互补问题转化为与之等价的方程组,再在每次迭代中使用非精确光滑牛顿法近似地求解该方程组。在较弱的条件下,证明了算法具有全局和局部二阶收敛性。数值结果表明,该算法对求解线性圆锥互补问题是有效的。Under the standard inner product,the circular cone is usually nonsymmetric cone,which brings a great challenge to design the algorithm of circular cone complementarity problems,thus how to find good algorithms to solve circular cone complementarity problems is a hot issue.In this paper,Under the framework of smoothing Newton methods,an inexact smoothing Newton method for linear circular cone complementarity problems is proposed.Based on a new smoothing function of circular cone complementarity function,we reformulate the linear circular cone complementarity problem as a system of equations.Next the proposed algorithm solves this system of equations approximately in each iteration by using an inexact smoothing Newton method.Under suitable conditions,the proposed algorithm is shown to be globally and locally quadratically convergent.Finally,Numerical results demonstrate the effectiveness of the new algorithm for linear circular cone complementarity problems.

关 键 词：线性圆锥互补问题 非精确 光滑牛顿法 

分 类 号：O221[理学—运筹学与控制论]