Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming
Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming
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DOI：
10.1137/080739124
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发表时间：
2009-08
期刊：
影响因子：
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通讯作者：
D. H. Fang;Chong Li;K. Ng
中科院分区：
文献类型：
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作者：
D. H. Fang;Chong Li;K. Ng
对于由一个可能无穷族的真函数族(不一定是下半连续的)定义的一个不等式系统，我们引入了一些关于这些函数的共轭图形的约束限定的新概念。在新的约束条件下，我们得到了作为约束系统结果的逆凸不等式的刻画，并给出了稳定的Farkas引理成立的充要条件。类似地，我们给出了约束极小化问题具有强稳定拉格朗日对偶或强稳定拉格朗日对偶的刻画。推广和改进了圆锥规划问题中的几个已知结果。
For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which are a consequence of the constrained system, and we provide necessary and/or sufficient conditions for a stable Farkas lemma to hold. Similarly, we provide characterizations for constrained minimization problems to have the strong or strong stable Lagrangian dualities. Several known results in the conic programming problem are extended and improved.