二阶锥权互补问题的非精确非内点连续化算法  

An Inexact Non-Interior Continuation Algorithm for the Weighted Second-Order Cone Complementarity Problem

作　　者：曾荣 ZENG Rong(Academy of foundational Education,Neusoft Institute Guangdong,Foshan 528000,China)

机构地区：[1]广东东软学院基础教学院,广东佛山528000

出　　处：《大学数学》2021年第4期10-16,共7页College Mathematics

摘　　要：基于二阶锥权互补函数,将二阶锥权互补问题转化为一个方程组,运用非精确非内点连续化算法求解该方程组.该算法能以任意点作为初始点,且每次迭代时至多求解一个方程组.为节省算法求解方程组时的计算时间和内存,将非精确牛顿法引入到算法中.在适当假设下,证明了该算法是全局与局部二阶收敛的.最后数值实验表明了算法的良好性能.Based on the weighted second-order cone complementarity function,the weighted second-order cone complementarity problem is reformulated as a system of equations,and the inexact non-interior continuation algorithm is presented for solving this system of equations.The proposed algorithm can take an arbitrary point as the initial point and solves at most one system of equations at each iteration.In order to save the iterative calculation work time and memory,the inexact Newton method is used in the algorithm.Under suitable assumptions,the algorithm is shown to be globally and locally quadratically convergent.Finally,numerical experiments demonstrate that the good performance of the algorithm.

关 键 词：二阶锥权互补问题 非精确牛顿法 非内点连续化算法 全局收敛 局部二阶收敛 

分 类 号：O224[理学—运筹学与控制论]