多目标半定规划的Lagrange对偶与鞍点定理  

Lagrange Duality and Saddle Points Theorem for Multiobjective Semidefinite Programming

作　　者：李超[1] 王晓敏[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《上海交通大学学报》2005年第10期1733-1736,共4页Journal of Shanghai Jiaotong University

摘　　要：主要研究含矩阵函数半定约束和向量函数等式约束以及多个目标函数的多目标半定规划的对偶和鞍点问题.首先在似凸条件下建立了一个含矩阵函数半定约束系统的择一性定理,由此得到多目标半定规划及其在弱有效解意义下的Lagrange对偶理论,包括弱对偶、强对偶和逆对偶等.然后利用鞍点的等价定义,得到多目标半定规划的鞍点最优性条件.The paper studied the multiobjective semidefinite programming with a semidefinite constraint of a matrix function and a multiobjective function. In the sense of weak effective solution, the problems of Lagrange duality and saddle point are discussed under the eonvexlike condition. An alternative theorem of the system containing a semidefinite constraint of a matrix function is established at first. Duality theorem and saddle point optimality condition for the multiobjective semidefinite programming are then established.

关 键 词：多目标半定规划 弱有效解 似凸函数 LAGRANGE对偶 鞍点 

分 类 号：O224[理学—运筹学与控制论]