修正增广拉格朗日函数凸半无限规划的对偶定理  

Duality Theorem of Convex Semi-infinite Programming of Modified Augmented Lagrange Function

作　　者：许春 苏珂[1] 任乐乐 

机构地区：[1]河北大学数学与信息科学学院,河北保定071002

出　　处：《河南科技大学学报（自然科学版）》2018年第4期88-93,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(61572011);河北省自然科学基金项目(A2018201172);河北省教育厅重点基金项目(ZD2015069)

摘　　要：针对凸半无限规划问题,构造了新的修正增广拉格朗日函数,并且利用该修正增广拉格朗日函数,对凸半无限规划的对偶性进行了讨论。证明了在合理的假设条件下,凸半无限规划问题与其拉格朗日对偶问题间强对偶性成立,并举例说明了定理的有效性。A modified augmented Lagrange function was constructed to solve convex semi-infinite programming problem. The duality of convex semi-infinite programming was discussed by using the modified augmented Lagrange function. Under the reasonable assumed conditions,the strong duality between convex semi-infinite programming problem and its Lagrange dual problem was proved. An example was given to illustrate the validity of the theorem.

关 键 词：半无限规划 凸函数 拉格朗日对偶 共轭函数 对偶间隙 

分 类 号：O221.2[理学—运筹学与控制论]