On linear-quadratic elliptic control problems of semi-infinite type


Abstract:

We derive a priori error estimates for linear-quadratic elliptic optimal control problems with pointwise state constraints in a compact subdomain of the spatial domain Ω for a class of problems with finite-dimensional control space. The problem formulation leads to a class of semi-infinite programming problems, whose constraints are implicitly given by the FE-discretization of the underlying PDEs. We prove an order of h√{pipe}log h{pipe} for the error {pipe}ū - ūh{pipe} in the controls, and show that it can be improved to an order of h2{pipe}log h{pipe} under certain assumptions on the structure of the active set. Numerical experiments underline the proven theoretical results. © 2011 Taylor & Francis.

Año de publicación:

2011

Keywords:

  • error estimates
  • Elliptic optimal control problem
  • State constraints
  • Finite element discretization
  • Semi-infinite optimization

Fuente:

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scopusscopus

Tipo de documento:

Article

Estado:

Acceso restringido

Áreas de conocimiento:

  • Control óptimo
  • Optimización matemática

Áreas temáticas:

  • Análisis