TY - GEN A1 - Clason, Christian A1 - Deng, Yu A1 - Mehlitz, Patrick A1 - Prüfert, Uwe T1 - Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method T2 - Optimization Methods and Software N2 - A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space. After deriving necessary optimality conditions of strong stationarity-type, a penalty method based on the Fischer–Burmeister function is suggested and its theoretical properties are analyzed. Finally, the numerical treatment of the problem is discussed and results of computational experiments are presented. KW - Fischer–Burmeister function KW - mathematical problems with complementarity constraints KW - optimal control KW - optimality conditions KW - penalty method Y1 - 2020 U6 - https://doi.org/10.1080/10556788.2019.1604705 SN - 1055-6788 SN - 1029-4937 VL - 35 IS - 1 SP - 142 EP - 170 ER - TY - GEN A1 - Deng, Yu A1 - Mehlitz, Patrick A1 - Prüfert, Uwe T1 - On an optimal control problem with gradient constraints T2 - Optimization N2 - Usually, control functions in control-constrained optimal control are chosen from a Lebesgue space. This choice, however, makes it impossible to postulate additional conditions on the control function's slope which is practically relevant in some situations. In order to overcome this disadvantage, a natural assumption would be to demand at least first-order Sobolev regularity for control functions. The present paper is devoted to the study of an elliptic optimal control problem whose control function is chosen from a Sobolev space and has to satisfy additional equality constraints on its weak gradient. Noting that the associated Karush–Kuhn–Tucker conditions do not provide a necessary optimality condition for the underlying optimal control problem in general, one cannot simply solve the problem of interest by considering the system of first-order optimality conditions. Instead a penalization procedure with strong convergence properties for the computational solution is suggested and its computational implementation is studied in detail. Particularly, some essential difficulties arising from the gradient constraints which do not appear in standard optimal control are discussed. KW - Control gradient constraints KW - enforcement phenomena in FEM KW - optimal control KW - optimality conditions KW - penalty method Y1 - 2020 U6 - https://doi.org/10.1080/02331934.2019.1604707 SN - 0233-1934 SN - 1029-4945 VL - 69 IS - 3 SP - 519 EP - 551 ER -