非凸半定规划的增广Lagrangian的微分的计算(英文)  

Calculating the Differential of the Augmented Lagrangian for Nonconvex SDP

作　　者：张宏伟[1] 张立卫[1] 

机构地区：[1]大连理工大学应用数学系,大连116024

出　　处：《运筹学学报》2004年第3期66-70,共5页Operations Research Transactions

基　　金：PartlysupportedbyTheFoundsofYoungScientistsofChina,No.10001007partlysupposedbytheStateFoundationsofPh.DUnits,No.20020141013

摘　　要：迄今为止,还未见出版过有关求解非凸半定规划的算法,但在最近,Chen,et.al(2000)和Sun & Sun(1999)关于非凸半定规划(SDP)的增广Lagrangian的研究是非常有用的,在本文中,我们证明非凸半定规划的增广Lagrangian是可微的,并且给出它的可微表达式。So far there have been no published results on algorithms for solving nonconvex semidef-inite programming (SDP) problems. Recently, we found that the differential theories developed by Chen, et.al(2000) and Sun & Sun(1999) are very useful in the study of the augmented Lagrange algorithm for solving the nonconvex semidefinite problems. In this note, we prove that the augmented Lagrangian is differentiable and give the formula of the differential of the augmented Lagrangian.

关 键 词：非凸半定规划 增广Lagrangian 可微性 微分方程 

分 类 号：O175.2[理学—数学]