求解圆锥规划的光滑牛顿法  

A Smoothing Newton Algorithm for Circular Cone Programming

作　　者：韦洪锦 刘博[1] 迟晓妮[1] 万仲平[2] WEI Hong-jin LIU Bo CHI Xiao-ni WAN Zhong -ping(School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西高校数据分析与计算重点实验室,广西桂林541004 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学的实践与认识》2017年第10期152-160,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11401126,71471140);广西自然科学基金(2016GXNSFBA380102,2014GXNSFFA118001);国家级大学生创新创业计划项目(201610595037)

摘　　要：圆锥规划是一类重要的非对称锥优化问题.基于一个光滑函数,将圆锥规划的最优性条件转化成一个非线性方程组,然后给出求解圆锥规划的光滑牛顿法.该算法只需求解一个线性方程组和进行一次线搜索.运用欧几里得约当代数理论,证明该算法具有全局和局部二阶收敛性.最后数值结果表明算法的有效性.In this paper, we consider the circular cone programming, which is a kind of important nonsymmetric cone optimization problem. Based on a smoothing function, we re- formulate the optimality conditions of the circular cone programming as a system of nonlinear equations, and propose a smoothing Newton method for solving circular cone programming problem. The algorithm solves only one linear system of equations approximately and performs only one line search at each iteration. The proposed algorithm is shown to be globally and locally quadratically convergent by using the Euclidean Jordan algebra theory. Finally, numerical results illustrate the effectiveness of our new algorithm.

关 键 词：圆锥规划 光滑牛顿法 光滑函数 局部二阶收敛性 

分 类 号：O224[理学—运筹学与控制论]