Optimal control of parabolic problems with state constraints: A penalization method for optimality conditions
The author studies state constrained optimal control problems with parabolic evolution equations. Optimality conditions are derived where the state and control expressions have been decoupled. The approach used is to consider a family of problems where deviation of the dynamics from feasibility is penalized through a parameter \(\varepsilon\). Decoupled optimality conditions are determined for each of these problems. Using Slater-like assumptions the limit of these optimality conditions provide optimality conditions for the original problem and the existence of Lagrange multipliers. The method is demonstrated on a distributed control problem with a Dirichlet boundary condition, and a boundary control problem with a Neumann boundary condition.
scientific article; zbMATH DE number 563450
scientific article