Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the distance between polytopes

Author: Leopold B. Willner
Journal: Quart. Appl. Math. 26 (1968), 207-212
MSC: Primary 41.60
DOI: https://doi.org/10.1090/qam/231106
MathSciNet review: 231106
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is written to fill an apparent gap in the literature in connection with some elementary problems of distance in finite dimensional normed linear spaces. In particular the problem of determining the distance between two polytopes in a normed $ n$-dimensional real vector space is considered. Special consideration is given to the case in which the norm is a twice differentiable function of its arguments and for this case a convex programming algorithm is presented. In addition several other cases are considered including the well known discrete Tchebycheff approximation. The results should find application in approximation theory.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 41.60

Retrieve articles in all journals with MSC: 41.60

Additional Information

DOI: https://doi.org/10.1090/qam/231106
Article copyright: © Copyright 1968 American Mathematical Society

American Mathematical Society