Abstract

The article considers differential inclusion with a given set-valued mapping and initial point. It is required to find a solution of this differential inclusion that minimizes an integral functional. Some classical results about the maximum principle for differential inclusions are obtained using the support and exact penalty functions. This is done for differentiable and for non-differentiable set-valued mappings in phase variables.

Original languageEnglish
Article number309
Number of pages13
JournalElectronic Journal of Differential Equations
Volume2015
Issue number309
Publication statusPublished - 21 Dec 2015

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Exact Penalty
Differential Inclusions
Set-valued Mapping
Exact Penalty Function
Functional Integral
Maximum Principle
Differentiable
Minimise

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title = "DIFFERENTIAL INCLUSIONS AND EXACT PENALTIES",
abstract = "The article considers differential inclusion with a given set-valued mapping and initial point. It is required to find a solution of this differential inclusion that minimizes an integral functional. Some classical results about the maximum principle for differential inclusions are obtained using the support and exact penalty functions. This is done for differentiable and for non-differentiable set-valued mappings in phase variables.",
keywords = "Nonsmooth functional, differential inclusion, support function, exact penalty function, maximum principle, OPTIMIZATION",
author = "A.V. Fominyh and V.V. Karelin and L.N. Polyakova",
year = "2015",
month = "12",
day = "21",
language = "Английский",
volume = "2015",
journal = "Electronic Journal of Differential Equations",
issn = "1072-6691",
publisher = "Texas State University - San Marcos",
number = "309",

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T1 - DIFFERENTIAL INCLUSIONS AND EXACT PENALTIES

AU - Fominyh, A.V.

AU - Karelin, V.V.

AU - Polyakova, L.N.

PY - 2015/12/21

Y1 - 2015/12/21

N2 - The article considers differential inclusion with a given set-valued mapping and initial point. It is required to find a solution of this differential inclusion that minimizes an integral functional. Some classical results about the maximum principle for differential inclusions are obtained using the support and exact penalty functions. This is done for differentiable and for non-differentiable set-valued mappings in phase variables.

AB - The article considers differential inclusion with a given set-valued mapping and initial point. It is required to find a solution of this differential inclusion that minimizes an integral functional. Some classical results about the maximum principle for differential inclusions are obtained using the support and exact penalty functions. This is done for differentiable and for non-differentiable set-valued mappings in phase variables.

KW - Nonsmooth functional

KW - differential inclusion

KW - support function

KW - exact penalty function

KW - maximum principle

KW - OPTIMIZATION

M3 - статья

VL - 2015

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

IS - 309

M1 - 309

ER -