Upper bounds for the constants of Bennett's inequality and the Gale–Berlekamp switching game

IF 0.8 3区数学 Q2 MATHEMATICS Mathematika Pub Date : 2023-10-27 DOI:10.1112/mtk.12229

Daniel Pellegrino, Anselmo Raposo Jr.

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Abstract

In 1977, G. Bennett proved, by means of nondeterministic methods, an inequality that plays a fundamental role in a series of optimization problems. More precisely, Bennett's inequality shows that, for $p_{1}, p_{2} \in [1, \infty]$ and all positive integers $n_{1}, n_{2}$ , there exists a bilinear form $A_{n_{1}, n_{2}} : (R^{n_{1}} {, ∥ \cdot ∥}_{p_{1}}) \times (R^{n_{2}} {, ∥ \cdot ∥}_{p_{2}}) ⟶ R$ with coefficients ±1 satisfying

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Bennett不等式常数的上界和Gale-Berlekamp交换对策

1977年，G. Bennett用不确定性方法证明了一个不等式，这个不等式在一系列优化问题中起着基本的作用。更准确地说，Bennett不等式表明，对于p1, p2∈[1]，∞]$p_{1},p_{2} \in [1,\infty ]$和所有正整数n1, n2 $n_{1},n_{2}$，存在双线性形式a n 1, n 2(R n 1，∥·∥p 1) × (R n 2，∥·∥p 2) R $A_{n_{1},n_{2}}\colon (\mathbb {R}^{n_{1}},\Vert \cdot \Vert _{p_{1}}) \times (\mathbb {R}^{n_{2}},\Vert \cdot \Vert _{p_{2}}) \longrightarrow \mathbb {R}$，系数±1令人满意

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.

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