Directional Differentiability, Coexhausters, Codifferentials and Polyhedral DC Functions

Standard

Directional Differentiability, Coexhausters, Codifferentials and Polyhedral DC Functions. / Abbasov, Majid E. .

в: Taiwanese Journal of Mathematics, 12.2022, стр. 1-17.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{6b8cf2f4f09e424db70d7ec31322905e,

title = "Directional Differentiability, Coexhausters, Codifferentials and Polyhedral DC Functions",

abstract = "Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codifferentials, the theories of these two concepts continue to develop simultaneously. Moreover, codifferentials and coexhausters are strongly connected with DC functions. In this paper we trace analogies between all these objects, and prove the equivalence of the boundedness and optimality conditions described in terms of these notions. This allows one to extend the results derived in terms of one object to the problems stated via the other one. Another contribution of this paper is the study of connection between nonhomogeneous approximations and directional derivatives and formulate optimality conditions in terms of nonhomogeneous approximations.",

keywords = "codifferentials, coexhausters, constructive nonsmooth analysis, DC functions, polyhedral functions",

author = "Abbasov, {Majid E.}",

note = "Majid E. Abbasov. {"}Directional Differentiability, Coexhausters, Codifferentials and Polyhedral DC Functions.{"} Taiwanese J. Math. Advance Publication 1 - 17, 2022. https://doi.org/10.11650/tjm/221201",

year = "2022",

month = dec,

language = "English",

pages = "1--17",

journal = "Taiwanese Journal of Mathematics",

issn = "1027-5487",

publisher = "Mathematical Society of the Rep. of China",

}

RIS

TY - JOUR

T1 - Directional Differentiability, Coexhausters, Codifferentials and Polyhedral DC Functions

AU - Abbasov, Majid E.

N1 - Majid E. Abbasov. "Directional Differentiability, Coexhausters, Codifferentials and Polyhedral DC Functions." Taiwanese J. Math. Advance Publication 1 - 17, 2022. https://doi.org/10.11650/tjm/221201

PY - 2022/12

Y1 - 2022/12

N2 - Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codifferentials, the theories of these two concepts continue to develop simultaneously. Moreover, codifferentials and coexhausters are strongly connected with DC functions. In this paper we trace analogies between all these objects, and prove the equivalence of the boundedness and optimality conditions described in terms of these notions. This allows one to extend the results derived in terms of one object to the problems stated via the other one. Another contribution of this paper is the study of connection between nonhomogeneous approximations and directional derivatives and formulate optimality conditions in terms of nonhomogeneous approximations.

AB - Codifferentials and coexhausters are used to describe nonhomogeneous approximations of a nonsmooth function. Despite the fact that coexhausters are modern generalizations of codifferentials, the theories of these two concepts continue to develop simultaneously. Moreover, codifferentials and coexhausters are strongly connected with DC functions. In this paper we trace analogies between all these objects, and prove the equivalence of the boundedness and optimality conditions described in terms of these notions. This allows one to extend the results derived in terms of one object to the problems stated via the other one. Another contribution of this paper is the study of connection between nonhomogeneous approximations and directional derivatives and formulate optimality conditions in terms of nonhomogeneous approximations.

KW - codifferentials

KW - coexhausters

KW - constructive nonsmooth analysis

KW - DC functions

KW - polyhedral functions

M3 - Article

SP - 1

EP - 17

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

ER -

ID: 100951845