Existence and relaxation for subdifferential inclusions with unbounded perturbation

Sergey A. Timoshin

doi:10.1007/s10107-016-1104-5

Existence and relaxation for subdifferential inclusions with unbounded perturbation

Sergey A. Timoshin^*

^*Corresponding author for this work

RAS - Matrosov Institute for System Dynamics and Control Theory, Siberian Branch

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

2 Citations (Scopus)

Abstract

We consider a differential inclusion of subdifferential type with a nonconvex and unbounded valued perturbation. Existence and relaxation results are obtained for this inclusion. By relaxation we mean approximation of a solution of the differential inclusion with convexified perturbation by solutions of the given inclusion. The traditional condition of Lipschitz continuity for such kind of problems is weakened and a somehow more appropriate in the context of unbounded valued multifunctions “truncated” version of it is considered instead.

Original language	English
Pages (from-to)	65-85
Number of pages	21
Journal	Mathematical Programming
Volume	166
Issue number	1-2
DOIs	https://doi.org/10.1007/s10107-016-1104-5
Publication status	Published - 1 Nov 2017
Externally published	Yes

Keywords

Evolution inclusion
Perturbation
Relaxed Lipschitz condition
Subdifferential
Unbounded right-hand side

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abstract = "We consider a differential inclusion of subdifferential type with a nonconvex and unbounded valued perturbation. Existence and relaxation results are obtained for this inclusion. By relaxation we mean approximation of a solution of the differential inclusion with convexified perturbation by solutions of the given inclusion. The traditional condition of Lipschitz continuity for such kind of problems is weakened and a somehow more appropriate in the context of unbounded valued multifunctions “truncated” version of it is considered instead.",

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AB - We consider a differential inclusion of subdifferential type with a nonconvex and unbounded valued perturbation. Existence and relaxation results are obtained for this inclusion. By relaxation we mean approximation of a solution of the differential inclusion with convexified perturbation by solutions of the given inclusion. The traditional condition of Lipschitz continuity for such kind of problems is weakened and a somehow more appropriate in the context of unbounded valued multifunctions “truncated” version of it is considered instead.

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KW - Perturbation

KW - Relaxed Lipschitz condition

KW - Subdifferential

KW - Unbounded right-hand side

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Existence and relaxation for subdifferential inclusions with unbounded perturbation

Abstract

Keywords

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