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.
0引言考虑如下的凸半无限规划(semi-infinite programming,SIP)问题:minf(x),s.t.g(x,w)≤0,w∈Ω,(1)x∈Rn其中:Ω为Rn中一闭集;f:Rn→R∪{∞}为广义实值凸函数;对每个w∈Ω,g:Rn×R→R关于变量x是凸函数。半无限规划问题的一个特例为线性半无限规划(linear semi-infinite pro
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