In this talk, we discuss second-order optimality conditions for optimal
control problems. This analysis is very important when we study the stability of the solution to the control problem with respect to small perturbations of the data. It is also crucial for proving superlinear or quadratic convergence of numerical algorithms for solving the problem, as well as for proving error estimates for numerical discretization of the control problem. We begin by establishing the analogies and differences between the optimality conditions for finite and infinite dimensional optimization problems. Then, an optimal control problem of a semilinear parabolic equation is considered. We highlight the difference between problems that do or do not involve the Tikhonov term in the cost
functional.

Zoom meeting: Link