Convex Functions in ACL2(r)

• Main Authors: Carl Kwan, Mark R. Greenstreet
• Format: Article
• Language: English
• Published: Open Publishing Association 2018-10-01
• Series: Electronic Proceedings in Theoretical Computer Science
• Online Access: http://arxiv.org/pdf/1810.04316v1

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.