约束优化问题的一种对偶性刻画  

The duality framework for constrained optimization problems

作　　者：王炜[1] 姜珊[1] 袁笑宇[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2011年第1期10-12,共3页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁省教育厅高等学校科研项目(2008376)

摘　　要：首先对一类集合,从两个不同的侧面刻画了集合沿某个方向的极小极大问题,并阐述了极小值与极大值相等的条件.对应于经典的优化问题,借助于目标函数的上图,将原问题与对偶问题对应于某个集合的极小极大问题,得到强对偶定理.最后,对Hilbert空间上的一类约束优化问题进行了刻画,得到了这一类约束优化问题的强对偶定理,进而可以通过对偶问题求解原问题.For a nonempty subset in R^n＋1,two simple optimization problems are firstly constructed from the necessary and sufficient conditions for the attainments and equality of the optimal values in Duality Theorems.These problems will be used as an analytical framework for constrained optimization duality.Corresponding to the classical optimization problem,by means of the epigraph of the objective function,the original problem and its dual problem as the minimax problems of a set,the strong duality theorem is obtained.Finally,a class of constrained optimization problems in Hilbert space are characterized,and it can be solved by dealing with its dual problem.

关 键 词：极小极大问题 对偶定理 约束优化 共轭函数 

分 类 号：O221.2[理学—运筹学与控制论]