On the intersection of a Clarke cone with a Boltyanskii cone

Alberto Bressan

doi:10.1137/060654852

On the intersection of a Clarke cone with a Boltyanskii cone

Alberto Bressan

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

6 Scopus citations

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 language	English (US)
Pages (from-to)	2054-2064
Number of pages	11
Journal	SIAM Journal on Control and Optimization
Volume	45
Issue number	6
DOIs	https://doi.org/10.1137/060654852
State	Published - 2007

All Science Journal Classification (ASJC) codes

Control and Optimization
Applied Mathematics

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10.1137/060654852

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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",

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

AU - Bressan, Alberto

PY - 2007

Y1 - 2007

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 - https://www.scopus.com/pages/publications/36448972008

UR - https://www.scopus.com/pages/publications/36448972008#tab=citedBy

U2 - 10.1137/060654852

DO - 10.1137/060654852

M3 - Article

AN - SCOPUS:36448972008

SN - 0363-0129

VL - 45

SP - 2054

EP - 2064

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 6

ER -

On the intersection of a Clarke cone with a Boltyanskii cone

Abstract

All Science Journal Classification (ASJC) codes

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