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arXiv · 1810.04316

Convex Functions in ACL2(r)

Carl Kwan·Mark R. Greenstreet
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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.

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Carl Kwan, Mark R. Greenstreet. 2018-10-10. Convex Functions in ACL2(r). https://doi.org/10.4204/eptcs.280.10

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