Sufficient approximate optimality condition for the inverse one-phase Stefan problem - Lipnicka, Marta; Lipnicki, Artur; Nowakowski, Andrzej (Control and cybernetics, 2024)
We investigate the identification problem for the one-phase Stefan problem. As the inverse Stefan problem is not well posed, an optimal control problem is considered instead. In the paper we develop a dual dynamic programming approach to derive sufficient approximate optimality conditions for that optimal control problem. As a next step we formulate and prove a verification theorem for approximate solution. The verification Theorem 4.1 is the basis for the development of a numerical algorithm. Having the verification theorem we do not need the convergence of our algorithm.