Fictitious Controls and Approximation of an Optimal Control Problem for Perona-Malik Equation
| Autor: | Peter Kogut, Yaroslav Kohut, Rosanna Manzo |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Optimization, Differential Equations and Their Applications, Vol 30, Iss 1, Pp 42-70 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2617-0108 2663-6824 |
| DOI: | 10.15421/142202 |
| Popis: | We discuss the existence of solutions to an optimal control problem for the Cauchy-Neumann boundary value problem for the evolutionary Perona-Malik equations. The control variable v is taken as a distributed control. The optimal control problem is to minimize the discrepancy between a given distribution ud 2 L2( ) and the current system state. We deal with such case of non-linearity when we cannot expect to have a solution of the original boundary value problem for each admissible control. Instead of this we make use of a variant of its approximation using the model with fictitious control in coefficients of the principle elliptic operator. We introduce a special family of regularized optimization problems for linear parabolic equations and show that each of these problems is consistent, well-posed, and their solutions allow to attain (in the limit) an optimal solution of the original problem as the parameter of regularization tends to zero. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
|