Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Exploring Convexity and its Uniqueness

Version 1 : Received: 12 October 2023 / Approved: 13 October 2023 / Online: 13 October 2023 (11:31:29 CEST)
Version 2 : Received: 13 October 2023 / Approved: 16 October 2023 / Online: 16 October 2023 (10:15:56 CEST)

How to cite: Diedrich, E. Exploring Convexity and its Uniqueness. Preprints 2023, 2023100882. https://doi.org/10.20944/preprints202310.0882.v2 Diedrich, E. Exploring Convexity and its Uniqueness. Preprints 2023, 2023100882. https://doi.org/10.20944/preprints202310.0882.v2

Abstract

This article explores the relationship between convex functions defined on integers ($\mathbb{Z}$) and their extension to real numbers ($\mathbb{R}$). We introduce key definitions and investigate the hypothesis that there exists a unique convex curve within this family of functions, leading to a proof by contradiction. Our findings highlight the preservation of convexity as functions transition from integers to real numbers.

Keywords

Convexity in N; Convexity in R; optimization; Suppor Vector Machines

Subject

Computer Science and Mathematics, Artificial Intelligence and Machine Learning

Comments (1)

Comment 1
Received: 16 October 2023
Commenter: Eduardo Diedrich
Commenter's Conflict of Interests: Author
Comment: I focuses on the Machine Learning field instead of the economic applications.
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