Name
Abstract | ||
|---|---|---|
We consider an optimal control problem that entails the minimization of a nondifferentiable cost functional, fractional diffusion as state equation and constraints on the control variable. We provide existence, uniqueness and regularity results together with first-order optimality conditions. In order to propose a solution technique, we realize fractional diffusion as the Dirichlet-to-Neumann map for a nonuniformly elliptic operator and consider an equivalent optimal control problem with a nonuniformly elliptic equation as state equation. The rapid decay of the solution to this problem suggests a truncation that is suitable for numerical approximation. We propose a fully discrete scheme: piecewise constant functions for the control variable and first-degree tensor product finite elements for the state variable. We derive a priori error estimates for the control and state variables. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1515/cmam-2017-0030 | COMPUTATIONAL METHODS IN APPLIED MATHEMATICS |
Keywords | Field | DocType |
Optimal Control Problem,Nondifferentiable Objective,Sparse Controls,Fractional Diffusion,Weighted Sobolev Spaces,Finite Elements,Stability,Anisotropic Estimates | Equation of state,Uniqueness,Mathematical optimization,Optimal control,Mathematical analysis,Elliptic operator,Control variable,State variable,Elliptic curve,Piecewise,Mathematics | Journal |
Volume | Issue | ISSN |
18 | 1 | 1609-4840 |
Citations | PageRank | References |
1 | 0.35 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Enrique Otárola | 1 | 86 | 13.91 |
| Abner J. Salgado | 2 | 105 | 13.27 |