On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations
Joint Authors
Kogut, Peter I.
Kupenko, Olha P.
Manzo, Rosanna
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-11-17
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
We discuss the existence issue to an optimal control problem for one class of nonlinear elliptic equations with an exponential type of nonlinearity.
We deal with the control object when we cannot expect to have a solution of the corresponding boundary value problem in the standard functional space for all admissible controls.
To overcome this difficulty, we make use of a variant of the classical Tikhonov regularization scheme.
In particular, we eliminate the PDE constraints between control and state and allow such pairs run freely by introducing an additional variable which plays the role of “compensator” that appears in the original state equation.
We show that this fictitious variable can be determined in a unique way.
In order to provide an approximation of the original optimal control problem, we define a special family of regularized optimization problems.
We show that each of these problems is consistent, well-posed, and their solutions allow to attain an optimal solution of the original problem as the parameter of regularization tends to zero.
As a consequence, we prove the existence of optimal solutions to the original problem and propose a way for their approximation.
American Psychological Association (APA)
Kogut, Peter I.& Kupenko, Olha P.& Manzo, Rosanna. 2020. On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations. Abstract and Applied Analysis،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1119933
Modern Language Association (MLA)
Kogut, Peter I.…[et al.]. On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations. Abstract and Applied Analysis No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1119933
American Medical Association (AMA)
Kogut, Peter I.& Kupenko, Olha P.& Manzo, Rosanna. On Regularization of an Optimal Control Problem for Ill-Posed Nonlinear Elliptic Equations. Abstract and Applied Analysis. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1119933
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119933