A closedness condition and its applications to DC programs with convex constraints
A closedness condition and its applications to DC programs with convex constraints
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DOI：
10.1080/02331930801951348
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发表时间：
2010-05
期刊：
影响因子：
2.2
通讯作者：
N. Dinh;T. Nghia;G. Vallet
中科院分区：
文献类型：
--
作者：
N. Dinh;T. Nghia;G. Vallet
本文讨论了一个涉及凸函数和凸约束系统的闭性条件（CC）。这类条件在凸优化问题的研究中起着重要的作用。我们的目标是建立这个条件的几个特征，并应用它们来研究锥凸约束和集合约束下的DC函数极小化问题。首先，我们建立了几个所谓的“Toland-Fenchel-拉格朗日”对偶定理。作为结果，各种版本的广义Farkas引理的对偶形式的系统涉及凸和DC功能的派生。然后，我们建立了凸约束下DC问题的最优性条件。给出了凸问题和凸约束下凸函数极大化问题的最优性条件。大多数结果是在（CC）条件下建立的。这篇文章作为一个链接最近发表的几个相应的已知的DC程序和凸规划。
This paper concerns a closedness condition called (CC) involving a convex function and a convex constrained system. This type of condition has played an important role in the study of convex optimization problems. Our aim is to establish several characterizations of this condition and to apply them to study problems of minimizing a DC function under a cone-convex constraint and a set constraint. First, we establish several so-called ‘Toland–Fenchel–Lagrange’ duality theorems. As consequences, various versions of generalized Farkas lemmas in dual forms for systems involving convex and DC functions are derived. Then, we establish optimality conditions for DC problem under convex constraints. Optimality conditions for convex problems and problems of maximizing a convex function under convex constraints are given as well. Most of the results are established under the (CC) condition. This article serves as a link between several corresponding known ones published recently for DC programs and for convex programs.