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Searching for and Quantifying Nonconvexity Regions of Functions*. / Davydov, Youri; Moldavskaya, Elina; Zitikis, Ričardas.

In: Lithuanian Mathematical Journal, Vol. 59, No. 4, 01.10.2019, p. 507-518.

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

Harvard

Davydov, Y, Moldavskaya, E & Zitikis, R 2019, 'Searching for and Quantifying Nonconvexity Regions of Functions*', Lithuanian Mathematical Journal, vol. 59, no. 4, pp. 507-518. https://doi.org/10.1007/s10986-019-09465-6

APA

Davydov, Y., Moldavskaya, E., & Zitikis, R. (2019). Searching for and Quantifying Nonconvexity Regions of Functions*. Lithuanian Mathematical Journal, 59(4), 507-518. https://doi.org/10.1007/s10986-019-09465-6

Vancouver

Davydov Y, Moldavskaya E, Zitikis R. Searching for and Quantifying Nonconvexity Regions of Functions*. Lithuanian Mathematical Journal. 2019 Oct 1;59(4):507-518. https://doi.org/10.1007/s10986-019-09465-6

Author

Davydov, Youri ; Moldavskaya, Elina ; Zitikis, Ričardas. / Searching for and Quantifying Nonconvexity Regions of Functions*. In: Lithuanian Mathematical Journal. 2019 ; Vol. 59, No. 4. pp. 507-518.

BibTeX

@article{112eb19c40d5407a8420b0536e735118,
title = "Searching for and Quantifying Nonconvexity Regions of Functions*",
abstract = "Convexity plays a prominent role in a number of areas, but practical considerations often lead to nonconvex functions. We suggest a method for determining regions of convexity and also for assessing the lack of convexity of functions in the other regions. The method relies on a specially constructed decomposition of symmetric matrices. Illustrative examples accompany theoretical results.",
keywords = "convex analysis, Hessian, nonconvexity, penalty function, risk assessment, Weyl inequality",
author = "Youri Davydov and Elina Moldavskaya and Ri{\v c}ardas Zitikis",
year = "2019",
month = oct,
day = "1",
doi = "10.1007/s10986-019-09465-6",
language = "English",
volume = "59",
pages = "507--518",
journal = "Lithuanian Mathematical Journal",
issn = "0363-1672",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Searching for and Quantifying Nonconvexity Regions of Functions*

AU - Davydov, Youri

AU - Moldavskaya, Elina

AU - Zitikis, Ričardas

PY - 2019/10/1

Y1 - 2019/10/1

N2 - Convexity plays a prominent role in a number of areas, but practical considerations often lead to nonconvex functions. We suggest a method for determining regions of convexity and also for assessing the lack of convexity of functions in the other regions. The method relies on a specially constructed decomposition of symmetric matrices. Illustrative examples accompany theoretical results.

AB - Convexity plays a prominent role in a number of areas, but practical considerations often lead to nonconvex functions. We suggest a method for determining regions of convexity and also for assessing the lack of convexity of functions in the other regions. The method relies on a specially constructed decomposition of symmetric matrices. Illustrative examples accompany theoretical results.

KW - convex analysis

KW - Hessian

KW - nonconvexity

KW - penalty function

KW - risk assessment

KW - Weyl inequality

UR - http://www.scopus.com/inward/record.url?scp=85075229256&partnerID=8YFLogxK

U2 - 10.1007/s10986-019-09465-6

DO - 10.1007/s10986-019-09465-6

M3 - Article

AN - SCOPUS:85075229256

VL - 59

SP - 507

EP - 518

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 4

ER -

ID: 49897572