KISSING POLYTOPES

Antoine Deza; Shmuel Onn; Sebastian Pokutta; Lionel Pournin

doi:10.1137/24M1640859

KISSING POLYTOPES

Antoine Deza, Shmuel Onn, Sebastian Pokutta, Lionel Pournin

Data and Decision Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed.

Original language	English
Pages (from-to)	2643-2664
Number of pages	22
Journal	SIAM Journal on Discrete Mathematics
Volume	38
Issue number	4
DOIs	https://doi.org/10.1137/24M1640859
State	Published - 2024

Keywords

alternating projections
distances in geometric lattices
facial distance
lattice polytopes
pyramidal width
vertex-facet distance

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1137/24M1640859

Cite this

@article{e5db062e83a24b10a1d4a5ab023c38cf,

title = "KISSING POLYTOPES",

abstract = "We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed.",

keywords = "alternating projections, distances in geometric lattices, facial distance, lattice polytopes, pyramidal width, vertex-facet distance",

author = "Antoine Deza and Shmuel Onn and Sebastian Pokutta and Lionel Pournin",

note = "Publisher Copyright: {\textcopyright} 2024 SIAM.",

year = "2024",

doi = "10.1137/24M1640859",

language = "אנגלית",

volume = "38",

pages = "2643--2664",

number = "4",

}

TY - JOUR

T1 - KISSING POLYTOPES

AU - Deza, Antoine

AU - Onn, Shmuel

AU - Pokutta, Sebastian

AU - Pournin, Lionel

PY - 2024

Y1 - 2024

N2 - We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed.

AB - We investigate the following question: How close can two disjoint lattice polytopes contained in a fixed hypercube be? This question stems from various contexts where the minimal distance between such polytopes appears in complexity bounds of optimization algorithms. We provide nearly matching bounds on this distance and discuss its exact computation. We also give similar bounds for disjoint rational polytopes whose binary encoding length is prescribed.

KW - alternating projections

KW - distances in geometric lattices

KW - facial distance

KW - lattice polytopes

KW - pyramidal width

KW - vertex-facet distance

UR - http://www.scopus.com/inward/record.url?scp=85206239897&partnerID=8YFLogxK

U2 - 10.1137/24M1640859

DO - 10.1137/24M1640859

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85206239897

SN - 0895-4801

VL - 38

SP - 2643

EP - 2664

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 4

ER -

KISSING POLYTOPES

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this