具有超线性收敛性的非线性半定规划的滤子算法  

Superlinear convergent filter method for nonlinear semidefinite programming

作　　者：赵奇 张燕 ZHAO Qi;ZHANG Yan(Department of Basic Education,Zhangjiagang Campus,Jiangsu University of Science and Technology,Zhangjiagang 215600,China)

机构地区：[1]江苏科技大学张家港校区基础教学部,张家港215600

出　　处：《江苏科技大学学报（自然科学版）》2018年第5期746-752,共7页Journal of Jiangsu University of Science and Technology:Natural Science Edition

摘　　要：滤子算法是计算非线性半定规划(nonlinear simidefinite programming,NLSDP)的一个有效方法,然而,和非线性规划类似,该方法也会产生Maratos效应,从而影响算法的超线性收敛性.文中提出了一个带二阶校正步的滤子算法,在适当的假设条件下,证明了该方法具有全局收敛性和超线性收敛性.此外,文中利用SDPT3软件包计算原理和子问题的最优性条件,得到了相关的乘子关系,从而应用于BFGS校正公式中.数值实验的例子表明该算法是稳定而有效的.In this article,we present a filter method with a second-order correction technique for NLSDP(nonlinear semidefinite programming).The global and local convergence is analyzed.By the optimality condition of SDPT3 package when solving the subproblem,we also derive the relevant multiplier expression formula of the BFGS correction.The numerical results show that the algorithm is robust and effective.

关 键 词：非线性半定规划 二阶校正步 SDPT3 超线性收敛性 

分 类 号：O221[理学—运筹学与控制论]