Locally Lipschitz stability of solutions to a parametric parabolic optimal control problem with mixed pointwise constraints (Q6622706)

Parametric optimal control is considered for semilinear parabolic boundary value problems with mixed inequality constraints. The parameters enter in the differential equation, the integral cost functional and the constraints. Under suitable regularity assumptions, if the strong second-order sufficient optimality condition is satisfied for given parameter, the solution is locally strong, and the optimal solutions (state and control) and corresponding Lagrange multipliers are locally Lipschitz continuous functions of the parameters. Sufficient conditions for the quadratic growth property of the cost functional are also proved.