一致Cartesian-P二阶锥权互补问题的非单调下降算法  

A Nonmonotone Descent Algorithm for the Uniform Cartesian-P Weighted Second-order Cone Complementarity Problem

作　　者：曾荣 迟晓妮[2] ZENG Rong;CHI Xiao-ni(School of Basic Education,Neusoft Institute Guangdong,Foshan 528000,China;School of Mathematics and Computing Science,Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]广东东软学院基础教学院,广东佛山528000 [2]桂林电子科技大学数学与计算科学学院广西密码学与信息安全重点实验室,广西桂林541004

出　　处：《数学的实践与认识》2021年第10期192-203,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11861026,11661002,71961004);广西自然科学基金(2016GXNSFBA380102);广西密码学与信息安全重点实验室研究课题(GCIS201819)。

摘　　要：运用下降算法求解二阶锥权互补问题.基于二阶锥权互补函数,构造一个价值函数,并在一致C artesian-P性质下证明该价值函数的强制性.运用该价值函数将二阶锥权互补问题转化为无约束最小化问题,提出求解二阶锥权互补问题的非单调下降算法.算法无需计算F(x)的雅可比矩阵,节省了迭代计算工作时间与内存.在单调性假设下,证明了算法全局收敛.最后数值实验表明算法是有效的.In this paper,the descent algorithm is presented for solving the weighted secondorder cone complementarity problem.Based on the weighted second-order cone complementarity function,a merit function is constructed.The coerciveness of merit function is proved under the uniform Cartesian-P property.We reformulate the weighted second-order cone complementarity problem as an unconstrained minimization problem by the merit function,and propose a nonmonotone descent algorithm for solving the weighted second-order cone complementarity problem.This algorithm does not need to calculate the Jacobian matrix of F(x),which saves computation work and memory in each iteration.Under monotonicity assumption,the algorithm is shown globally convergent.Some numerical experiments show that the algorithm is effective.

关 键 词：下降算法 二阶锥权互补问题 一致Cartesian-P性质 非单调线搜索 全局收敛 

分 类 号：O224[理学—运筹学与控制论]