Decidability of consistency of function and derivative information for a triangle and a convex quadrilateral
File(s)
Published version
Author(s)
Edalat, Abbas
Type
Report
Abstract
Given a triangle in the plane, a planar convex compact set and an upper and and a lower bound, we
derive a linear programming algorithm which checks if there exists a real-valued Lipschitz map defined
on the triangle and bounded by the lower and upper bounds, whose Clarke subgradient lies within the
convex compact set. We show that the problem is in fact equivalent to finding a piecewise linear surface
with the above property. We extend the result to a convex quadrilateral in the plane. In addition, we
obtain some partial results for this problem in higher dimensions.
derive a linear programming algorithm which checks if there exists a real-valued Lipschitz map defined
on the triangle and bounded by the lower and upper bounds, whose Clarke subgradient lies within the
convex compact set. We show that the problem is in fact equivalent to finding a piecewise linear surface
with the above property. We extend the result to a convex quadrilateral in the plane. In addition, we
obtain some partial results for this problem in higher dimensions.
Date Issued
2017-01-01
Citation
Departmental Technical Report: 17/7, 2017, pp.1-11
Publisher
Department of Computing, Imperial College London
Start Page
1
End Page
11
Journal / Book Title
Departmental Technical Report: 17/7
Copyright Statement
© 2017 The Author(s). This report is available open access under a CC-BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/)
Publication Status
Published
Article Number
17/7