@misc{Felgenhauer, author = {Felgenhauer, Ursula}, title = {A Newton-type method and optimality test for problems with bang-singular-bang optimal control}, series = {Pure and Applied Functional Analysis}, volume = {1}, journal = {Pure and Applied Functional Analysis}, number = {2}, pages = {197 -- 215}, abstract = {In the paper, a second-order method is investigated for control problems where the control has bang-singular-bang structure. To start with, the first-order system is formulated as a variational inequality including a differential equation for the switching function. For this system, a certain inexact Josephy-Newton method is considered. Under strong second-order sufficient conditions obtained via Goh's transformation of control and state-adjoint data, the local solvability is proved for the iterative problems. For so-called semilinear problems, locally the state and adjoint iterates converge superlinearly. The paper is completed by a Riccati test approach for verifying second-order optimality.}, language = {en} }