半定规划的两类对偶及最优性条件研究  

Study of Two Kinds of Duality and Optimality for Semidefinite Programming Problems

作　　者：席鸣晓 XI Mingxiao(College of Mathematics Sciences,Chongqing Nonnal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《湖北民族学院学报（自然科学版）》2018年第3期304-307,共4页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：重庆市自然科学基金项目(KJ1600316)

摘　　要：Langrange对偶理论是将约束优化问题转化为无约束优化问题,通过Langrange函数再作出对偶目标函数,而对偶目标函数提供原问题的下界,通过极大化对偶目标函数进而得到原问题的最优值.而广义Langrange对偶理论就是将传统的Langrange对偶的可行解区域给扩大,确定一些比较特殊的区域的方法,通过作出原函数的广义拉格朗日对偶问题进而给出半定规划的对偶定理以及最优性条件.最后研究了半定规划的共轭对偶理论并且给出了相应的对偶定理.Langrange duality theory makes constrained optimization problem into unconstrained optimization problem by Langrange function before making a dual objective function,the dual objective function provides the lower bound of the original problem,and the original problem is obtained by maximizing the dual objective function and the optimal value. And the generalized Langrange dual theory is to expand the feasible solution area of the traditional Langrange duality,to determine the methods of some special regions. In this paper,the dual theorem of semidefinite programming and the optimality condition are given by the generalized Lagrangian dual problem of the original function. Finally,the conjugate duality theory of semidefinite programming is studied and the corresponding duality theorem is given.

关 键 词：半定规划 广义拉格朗日对偶 共轭对偶 最优性条件 对偶理论 

分 类 号：O174[理学—数学]