Convex Functions in ACL2(r)

CoRR Pub Date : 2018-10-10 DOI:10.4204/EPTCS.280.10
Carl Kwan, M. Greenstreet
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引用次数: 4

Abstract

This paper builds upon our prior formalisation of R^n in ACL2(r) by presenting a set of theorems for reasoning about convex functions. This is a demonstration of the higher-dimensional analytical reasoning possible in our metric space formalisation of R^n. Among the introduced theorems is a set of equivalent conditions for convex functions with Lipschitz continuous gradients from Yurii Nesterov's classic text on convex optimisation. To the best of our knowledge a full proof of the theorem has yet to be published in a single piece of literature. We also explore "proof engineering" issues, such as how to state Nesterov's theorem in a manner that is both clear and useful.
ACL2(r)中的凸函数
本文建立在我们先前在ACL2(R)中对R^n的形式化的基础上,提出了一组关于凸函数的推理定理。这是在度量空间形式化的R^n中可能的高维分析推理的演示。在介绍的定理中,有一组来自yuri Nesterov关于凸优化的经典文本的具有Lipschitz连续梯度的凸函数的等价条件。据我们所知,这个定理的完整证明还没有在一篇文献中发表过。我们还探讨了“证明工程”问题,例如如何以一种既清晰又有用的方式陈述Nesterov定理。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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