Convexity of a small ball under quadratic map

Anatoly Dymarsky

doi:10.1016/j.laa.2015.09.005

Convexity of a small ball under quadratic map

Anatoly Dymarsky

Producción científica: Article › revisión exhaustiva

4 Citas (Scopus)

Resumen

We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak [1] in the case of a quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous term and provide a sufficient condition for its convexity.

Idioma original	English
Número de artículo	13356
Páginas (desde-hasta)	109-123
Número de páginas	15
Publicación	Linear Algebra and Its Applications
Volumen	488
DOI	https://doi.org/10.1016/j.laa.2015.09.005
Estado	Published - ene 1 2016

Nota bibliográfica

Publisher Copyright:
© 2015 Elsevier Inc.

Financiación

I would like to thank Tudor Dimofte, Konstantin Turitsyn and Jamin Sheriff for useful discussions and gratefully acknowledge support from the grant RFBR 15-01-04217 .

Financiadores	Número del financiador
Russian Foundation for Basic Research	15-01-04217

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Acceder al documento

10.1016/j.laa.2015.09.005

Otros archivos y enlaces

Citar esto

@article{16458144ec924ec79342501cdea3f1db,

title = "Convexity of a small ball under quadratic map",

abstract = "We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak [1] in the case of a quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous term and provide a sufficient condition for its convexity.",

keywords = "Convexity, Joint numerical range, Quadratic transformation (map), Trust region problem",

author = "Anatoly Dymarsky",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = jan,

day = "1",

doi = "10.1016/j.laa.2015.09.005",

language = "English",

volume = "488",

pages = "109--123",

}

TY - JOUR

T1 - Convexity of a small ball under quadratic map

AU - Dymarsky, Anatoly

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak [1] in the case of a quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous term and provide a sufficient condition for its convexity.

AB - We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak [1] in the case of a quadratic map. We also generalize the notion of the joint numerical range of m-tuple of matrices by adding vector-dependent inhomogeneous term and provide a sufficient condition for its convexity.

KW - Convexity

KW - Joint numerical range

KW - Quadratic transformation (map)

KW - Trust region problem

UR - http://www.scopus.com/inward/record.url?scp=84943329180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943329180&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2015.09.005

DO - 10.1016/j.laa.2015.09.005

M3 - Article

AN - SCOPUS:84943329180

SN - 0024-3795

VL - 488

SP - 109

EP - 123

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

M1 - 13356

ER -

Convexity of a small ball under quadratic map

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

Acceder al documento

Otros archivos y enlaces

Huella

Citar esto