求解非凸半定规划的一个非线性Lagrange算法及其收敛性分析(英文)  

Convergence Analysis of a Nonlinear Lagrange Algorithm for Nonconvex Semidefinite Programming

作　　者：刘勇进[1] 张立卫[2] 刘梅娇[1] 

机构地区：[1]沈阳航空工业学院理学系,沈阳110136 [2]大连理工大学应用数学系,116024

出　　处：《运筹学学报》2007年第4期5-14,共10页Operations Research Transactions

基　　金：Supported by the Youth NSF of China under project grant No. 10001007.

摘　　要：本文提出了一个求解非凸半定规划的非线性Lagrange算法,当二阶充分条件以及严格互补条件成立时,证明了这一算法的收敛性定理.收敛结果表明,当惩罚参数小于某个阀值时,算法是局部收敛的;此外,还给出了解的一个依赖于惩罚参数的误差界.This paper proposes a nonlinear Lagrange algorithm for solving nonconvex semidefinite programming. Under the second order sufficient condition and the strict complementarity condition, the convergence theorem is established. The convergence theorem shows that the nonlinear Lagrange algorithm is locally convergent when the penalty parameter is smaller than a threshold. The error bound of solution, depending on the penalty parameter, is also given.

关 键 词：运筹学 半定规划 非线性Lagrange算法 内点法 

分 类 号：O241.4[理学—计算数学] TP273.22[理学—数学]