Farkas-type results and duality for DC programs with convex constraints
Farkas-type results and duality for DC programs with convex constraints
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发表时间：
2007
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通讯作者：
N. Dinh;G. Vallet;T. Nghia
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作者：
N. Dinh;G. Vallet;T. Nghia
在本文中，我们感兴趣的是新版本的Farkas引理的系统涉及凸和DC-不等式。这些版本扩展了最近发表的著名的Farkas型结果，这些结果被用作凸优化问题研究的主要工具。这些结果被用来导出几个强对偶结果，如：DC和凸问题的拉格朗日，Fenchel-拉格朗日或Toland-Fenchel-拉格朗日对偶。此外，对这类问题，这些Farkas引理实际上等价于几个强对偶的拉格朗日，Fenchel-拉格朗日或TolandFenchel-拉格朗日型结果.
In this paper, we are interested in new versions of Farkas lemmas for systems involving convex and DC-inequalities. These versions extend well-known Farkas-type results published recently, which were used as main tools in the study of convex optimization problems. The results are used to derive several strong duality results such as: Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange duality for DC and convex problems. Moreover, it is shown that for this class of problems, these versions of Farkas lemma are actually equivalent to several strong duality results of Lagrange, Fenchel-Lagrange or TolandFenchel-Lagrange types.