解非凸半定规划问题的一个修正Lagrangian算法  

A Modified Lagrangian Method to the Nonconvex Semidefinite Programming Problems

作　　者：田媛[1] 田志远[1] 曹炜[1] 

机构地区：[1]青岛大学数学科学学院

出　　处：《青岛大学学报（自然科学版）》2008年第3期35-40,共6页Journal of Qingdao University(Natural Science Edition)

摘　　要：对于一般非凸半定规划,给出了一个修正Lagrangian函数及其相关算法,建立了参数解的误差估计式,并证明了算法的局部收敛性,即在适当条件下,罚参数存在一个阈值,当罚参数小于这一阈值时,由此修正Lagrangian算法产生的序列局部线性收敛到原问题的KKT点。This paper is devoted analyzing a modified Lagrangian method for the to general nonconvex semi- definite programming, which is an alogrithm based on a modified Lagrangian function. The error bound of the solutions with the penalty parameter is established. The local convergence of this method is also proved. It is showed that there exists a threshold of the penalty parameter such that the sequence products of the algorithm locally converge to the KKT point of the nonconvex semidefinite programming problem when the penalty parameter is less than the threshold.

关 键 词：非凸半定规划 Lagrangian算法 局部收敛性 

分 类 号：O221.2[理学—运筹学与控制论]