Alexander V. Fominyh, Vladimir V. Karelin, Lyudmila N. Polyakova
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.
Submitted July 23, 2015. Published December 21, 2015.
Math Subject Classifications: 34A60, 49J52.
Key Words: Nonsmooth functional; differential inclusion; support function;
exact penalty function; maximum principle.
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Alexander V. Fominyh Saint Petersburg State University 7-9, University emb., 199034 St. Petersburg, Russia email: alexfomster@mail.ru |
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Vladimir V. Karelin Saint Petersburg State University 7-9, University emb., 199034 St. Petersburg, Russia email: vlkarelin@mail.ru |
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Lyudmila N. Polyakova Saint Petersburg State University 7-9, University emb., 199034 St. Petersburg, Russia email: lnpol07@mail.ru |
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