Algorithms for PDE-constrained optimization. (English) Zbl 1207.49034
Summary: Some first and second order algorithmic approaches for the solution of PDE-constrained optimization problems are reviewed. An optimal control problem for the stationary Navier-Stokes system with pointwise control constraints serves as an illustrative example. Some issues in treating inequality constraints for the state variable and alternative objective functions are also discussed.
MSC:
| 49M05 | Numerical methods based on necessary conditions |
| 49M37 | Numerical methods based on nonlinear programming |
| 76D55 | Flow control and optimization for incompressible viscous fluids |
| 90C06 | Large-scale problems in mathematical programming |
| 49M15 | Newton-type methods |
Keywords:
PDE-constrained optimization; semi-smooth Newton method; control and state constraints; Navier-Stokes equationsReferences:
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