-convexity
-convexity
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DOI：
10.1080/02331930410001695283
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发表时间：
2004-04
期刊：
影响因子：
2.2
通讯作者：
W. Briec;C. Horvath
中科院分区：
文献类型：
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作者：
W. Briec;C. Horvath
给定一个同胚，我们可以在拓扑空间X上定义一个集合算子，通过公式。X上的这种凸性具有X上通常凸性的所有拓扑、几何和代数性质;直到变量改变，它是线性凸性。在凸分析和优化理论的背景下，Avriel（1972）和Ben Tal（1977）考虑了这种算子。我们考虑一个序列同胚和我们研究的抽象凸性是相关联的限制，在适当的意义下，序列的集合算子;我们称之为极限凸性凸性。我们可以粗略地说，这个非凸性是从通常的线性凸性通过形式替换得到的。最后，我们用一些简单的对偶和“最大规划”的应用来结束这篇文章。
Given a homeomorphism one can define on the topological space X a set operator through the formula . Such a convexity on X has all the topological, geometric and algebraic properties of the usual convexity on ; up to a change of variable, it is a linear convexity. In the context of convex analysis and optimization theory such operators were considered by Avriel (1972) and Ben Tal (1977). We consider a sequence on homeomorphisms and we study the abstract convexity which is associated to the limit, in the appropriate sense, of the sequence of set operators ; we call the limit-convexity -convexity. On one can loosely say that this -convexity is obtained from the usual linear convexity through the formal substitution . We end this article with some simple applications to duality and “max-programming”.