An optimal control problem for two-dimensional Schrödinger equation

In this paper we consider an optimal control problem controlled by three functions which are in the coefficients of a two-dimensional Schrödinger equation. After proving the existence and uniqueness of the optimal solution, we get the Frechet differentiability of the cost functional using Hamilton–P...

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Bibliographic Details
Published in:Applied mathematics and computation 2012-02, Vol.218 (11), p.6177-6187
Main Authors: Yagubov, Gabil, Toyoğlu, Fatma, Subaşı, Murat
Format: Article
Language:English
Subjects:
Hamilton–Pontryagin function
Inequalities
Mathematical analysis
Mathematical models
Optimal control
Optimal control problem
Optimization
Schroedinger equation
Schrödinger equation
Two dimensional
Uniqueness
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Summary:In this paper we consider an optimal control problem controlled by three functions which are in the coefficients of a two-dimensional Schrödinger equation. After proving the existence and uniqueness of the optimal solution, we get the Frechet differentiability of the cost functional using Hamilton–Pontryagin function. Then we state a necessary condition to an optimal solution in the variational inequality form using the gradient.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.12.028