Characterization of local quadratic growth for strong minima in the optimal control of semi-linear elliptic equations

In this article we consider an optimal control problem of a semi-linear elliptic equation, with bound constraints on the control. Our aim is to characterize local quadratic growth for the cost function J in the sense of strong solutions. This means that the function J growths quadratically over all feasible controls whose associated state is … Read more

Asymptotic expansion for the solution of a penalized control constrained semilinear elliptic problems

In this work we consider the optimal control problem of a semilinear elliptic PDE with a Dirichlet boundary condition, where the control variable is distributed over the domain and is constrained to be nonnegative. The approach is to consider an associated parametrized family of penalized problems, whose solutions define a central path converging to the … Read more