重庆理工大学学报（自然科学版）2018，Vol.32Issue(4)：204-211,8.DOI:10.3969/j.issn.1674-8425(z).2018.04.031
用离散化方法证明半定规划的拉格朗日强对偶定理
Proving Lagrangian Strong Duality Theorem of Semidefinite Programming Via a Discretization Approach
摘要
Abstract
It is reconsidered the proof of the strong duality theorem for semi-definite programming from an algorithmic perspective.Equivalent transformation between semidefinite programming and semiinfinite programming is firstly considered in this paper.The corresponding semi-infinite programming is then converted into a linear programming approximately via discretization method. Finally,based on the discretization method and its convergence property,we prove the Lagrangian strong duality theorem in the case of slater conditions satisfied for both the primal and the dual semi-definite programming problems.The proposed new proof enable us to design a new algorithm to solve the semi-definite programs via semi-infinite discretization methods.The convergence analysis of this newly designed discretization method is also considered.关键词
半定规划/半无限规划/离散化方法/拉格朗日强对偶定理Key words
semidefinite programming/semi-infinite programming/discretization method/Lagrangian strong duality theorem分类
数学引用本文复制引用
罗丹,罗洪林..用离散化方法证明半定规划的拉格朗日强对偶定理[J].重庆理工大学学报（自然科学版）,2018,32(4):204-211,8.基金项目
国家自然科学基金项目(11601050,11431004) （11601050,11431004）
重庆市教委项目(KJ1600316) （KJ1600316）
重庆市自然科学基金项目(cstc2016jcyjA0116) （cstc2016jcyjA0116）
