一个求解广义圆锥互补问题的光滑非精确牛顿法  

An Inexact Smoothing Newton Method for Solving General Circular Cone Complementarity Problems

作　　者：邵灿燃 汤京永 SHAO Canran;TANG Jingyong(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,Henan)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《四川师范大学学报（自然科学版）》2023年第2期239-246,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：河南省自然科学基金(222300420520);河南省高等学校重点科研项目(22A110020)。

摘　　要：研究一个求解广义圆锥互补问题的光滑非精确牛顿法.该算法基于一个新的光滑函数,将广义圆锥互补问题等价转化成一个光滑的非线性方程组,然后利用非精确牛顿法求解此方程组.算法在每次迭代时只需求解牛顿方程的一个近似解,因此适于求解大规模广义圆锥互补问题.在适当条件下,证明算法具有全局和局部二次收敛性质.数值实验结果表明算法是非常有效的.In this paper we study an inexact smoothing Newton method for solving the general circular cone complementarity problem.Based on a new smoothing function,we reformulate the general circular cone complementarity problem as a system of smooth nonlinear equations and propose an inexact Newton method to solve it.In each iteration,the proposed method solves the nonlinear equations only approximately and hence it is suitable to solve large scale general circular cone complementarity problems.Under suitable conditions,we prove that the proposed method has global and local quadratic convergence.Numerical results show that our algorithm is very effective.

关 键 词：广义圆锥互补问题 光滑函数 非精确牛顿法 二次收敛 

分 类 号：O221.1[理学—运筹学与控制论]