ABB定理：无限维的结果和限制。

IF 1.5 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2025-01-01 Epub Date: 2025-08-01 DOI:10.1007/s10957-025-02797-z

Aris Daniilidis, Carlo Alberto De Bernardi, Enrico Miglierina

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引用次数: 0

摘要

我们构造了一个关于格阶（n + 2）的具有孤立极大元的非空内部的弱紧凸子集。此外，极大点不能被任何严格正泛函所支持，这表明Arrow-Barankin-Blackwell定理是不成立的。这个例子揭示了圆锥有一个有界底的假设对于结果在无限维上的有效性的相关性。在后一种假设下，建立了严格极大性和极大性概念的等价性。

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ABB Theorems: Results and Limitations in Infinite Dimensions.

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ABB Theorems: Results and Limitations in Infinite Dimensions.

We construct a weakly compact convex subset of $ℓ^{2}$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $ℓ_{+}^{2}$ . Moreover, the maximal point cannot be supported by any strictly positive functional, which shows that the Arrow-Barankin-Blackwell theorem fails. This example discloses the pertinence of the assumption that the cone has a bounded base for the validity of the result in infinite dimensions. Under this latter assumption, the equivalence of the notions of strict maximality and maximality is established.

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来源期刊

Journal of Optimization Theory and Applications 数学-应用数学

CiteScore

3.30

自引率

5.30%

发文量

149

审稿时长

9.9 months

期刊介绍： The Journal of Optimization Theory and Applications is devoted to the publication of carefully selected regular papers, invited papers, survey papers, technical notes, book notices, and forums that cover mathematical optimization techniques and their applications to science and engineering. Typical theoretical areas include linear, nonlinear, mathematical, and dynamic programming. Among the areas of application covered are mathematical economics, mathematical physics and biology, and aerospace, chemical, civil, electrical, and mechanical engineering.