Half-space Representations of Piecewise Linear-Cubic Convex Functions

UBC Undergraduate Research

Half-space Representations of Piecewise Linear-Cubic Convex Functions Hatton, Jeffrey Davin

Abstract

This thesis documents the data structure and functions pertaining to storing piecewise linear-cubic convex functions in up to two dimensions as sets of half-spaces. Building upon the preexisting PLCVC class structure (a representation using vertices), the PLCHC library includes a constructor, return function, testing function, addition function, as well as helper functions. Given two PLCVC instances, the vertex/edge/face style of representing a function yields challenges to adding both functions. Storing PLCVC functions' domains as an ordered series of half-space inequalities facilitates the task. While such an application takes advantage of the PLCHC structure, PLCHC is not an appropriate structure for all operations. Thus, a return function, toPLCVC() is included to reconstruct an equivalent vertex representation of the function. Not all PLCVC vertices are extreme points, and are therefore arbitrary within restrictions. In order to unit test the return function, a custom comparator method was developed. The purpose being to eliminate arbitrary aspects from the evaluation, as well as to compensate for MATLAB floating point error within tolerance.

Item Metadata

Title	Half-space Representations of Piecewise Linear-Cubic Convex Functions
Creator	Hatton, Jeffrey Davin
Date Issued	2021-04
Description	This thesis documents the data structure and functions pertaining to storing piecewise linear-cubic convex functions in up to two dimensions as sets of half-spaces. Building upon the preexisting PLCVC class structure (a representation using vertices), the PLCHC library includes a constructor, return function, testing function, addition function, as well as helper functions. Given two PLCVC instances, the vertex/edge/face style of representing a function yields challenges to adding both functions. Storing PLCVC functions' domains as an ordered series of half-space inequalities facilitates the task. While such an application takes advantage of the PLCHC structure, PLCHC is not an appropriate structure for all operations. Thus, a return function, toPLCVC() is included to reconstruct an equivalent vertex representation of the function. Not all PLCVC vertices are extreme points, and are therefore arbitrary within restrictions. In order to unit test the return function, a custom comparator method was developed. The purpose being to eliminate arbitrary aspects from the evaluation, as well as to compensate for MATLAB floating point error within tolerance.
Subject	data structure; Linear-Cubic Convex Functions
Genre	Graduating Project
Type	Text
Language	eng
Series	University of British Columbia. COSC 449
Date Available	2021-06-07
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0398276
URI	http://hdl.handle.net/2429/78550
Affiliation	Science, Irving K. Barber Faculty of (Okanagan); Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)
Peer Review Status	Unreviewed
Scholarly Level	Undergraduate
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

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