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Data completion problems solved as Nash games
| Content Provider | Semantic Scholar |
|---|---|
| Author | Habbal, A. Kallel, M. |
| Copyright Year | 2011 |
| Abstract | Abstract. We consider the Cauchy problem for an elliptic operator, for mulated as a Nash game. The over specified Cauchy data are split among two playe rs : the first player solves the elliptic equation with the Dirichlet part of the Cauchy d ata prescribed over the accessible boundary, and a variable Neumann condition (which we call fir st player’s strategy) prescribed over the inaccessible part of the boundary. The second playe r makes use correspondingly of the Neumann part of the Cauchy data, with a variable Dirichle t condition prescribed over the inaccessible part of the boundary. The first player then mini izes the gap related to the non used Neumann part of the Cauchy data, and so does the second pl ayer with a corresponding Dirichlet gap. The two costs are coupled through a distribut ed field gaps. We prove that there exists always a unique Nash equilibrium, which turns out to b e the reconstructed data when the Cauchy problem has a solution. We also prove that the comp letion algorithm is stable with respect to noise. Some numerical 2D and 3D experiments a re provided to illustrate the efficiency and stability of our algorithm. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://hal.inria.fr/docs/00/64/87/12/PDF/HK-IP-415264.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Algorithm Class Code Exhibits as Topic Experiment Finite element method Kind of quantity - Equilibrium Mathematical optimization Missing data Nash equilibrium Numerical analysis Numerical stability Partial Published Comment Substance Withdrawal Syndrome c-Ha-ras p21 |
| Content Type | Text |
| Resource Type | Article |
