On the intersection of a Clarke cone with a Boltyanskii cone

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We provide an example of two closed sets S 1, S 2 ⊂ ℝ 4 such that S 1∩S 2 = {0}. Yet, at the origin, a Boltyanskii tangent cone C 1 to S 1 and the Clarke tangent cone C 2 to S 2 are strongly transversal. This settles a question originally proposed by H. Sussmann.

Original languageEnglish (US)
Pages (from-to)2054-2064
Number of pages11
JournalSIAM Journal on Control and Optimization
Volume45
Issue number6
DOIs
StatePublished - Dec 3 2007

Fingerprint

Tangent Cone
Cones
Cone
Intersection
Closed set

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Cite this

@article{f9b55d6d89034195ac39d4cd7e377d7f,
title = "On the intersection of a Clarke cone with a Boltyanskii cone",
abstract = "We provide an example of two closed sets S 1, S 2 ⊂ ℝ 4 such that S 1∩S 2 = {0}. Yet, at the origin, a Boltyanskii tangent cone C 1 to S 1 and the Clarke tangent cone C 2 to S 2 are strongly transversal. This settles a question originally proposed by H. Sussmann.",
author = "Alberto Bressan",
year = "2007",
month = "12",
day = "3",
doi = "10.1137/060654852",
language = "English (US)",
volume = "45",
pages = "2054--2064",
journal = "SIAM Journal on Control and Optimization",
issn = "0363-0129",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",

}

On the intersection of a Clarke cone with a Boltyanskii cone. / Bressan, Alberto.

In: SIAM Journal on Control and Optimization, Vol. 45, No. 6, 03.12.2007, p. 2054-2064.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the intersection of a Clarke cone with a Boltyanskii cone

AU - Bressan, Alberto

PY - 2007/12/3

Y1 - 2007/12/3

N2 - We provide an example of two closed sets S 1, S 2 ⊂ ℝ 4 such that S 1∩S 2 = {0}. Yet, at the origin, a Boltyanskii tangent cone C 1 to S 1 and the Clarke tangent cone C 2 to S 2 are strongly transversal. This settles a question originally proposed by H. Sussmann.

AB - We provide an example of two closed sets S 1, S 2 ⊂ ℝ 4 such that S 1∩S 2 = {0}. Yet, at the origin, a Boltyanskii tangent cone C 1 to S 1 and the Clarke tangent cone C 2 to S 2 are strongly transversal. This settles a question originally proposed by H. Sussmann.

UR - http://www.scopus.com/inward/record.url?scp=36448972008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36448972008&partnerID=8YFLogxK

U2 - 10.1137/060654852

DO - 10.1137/060654852

M3 - Article

AN - SCOPUS:36448972008

VL - 45

SP - 2054

EP - 2064

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 6

ER -