| Abstract: |
| In this talk, we consider some optimal control problem of an ODE governed by the hypergraph Laplacian, which is defined as a subdifferential of a convex function and then is a set-valued operator. In our previous works, we see that this ODE has some properties which resemble those of the PDEs with p-Laplacian. By using methods for a priori estimates, we can assure the existence of the optimal control for a suitable cost function. However, since the hypergraph Laplacian is a set-valued operator, it seems to be difficult to derive the necessary optimality condition for this problem. To cope with this difficulty, we introduce an approximation problem and assure the optimality condition for this. We also discuss the convergence of the condition to that for the original problem. |
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