### Project MATHEON C28

##### Full Title

Optimal control of phase separation phenomena.##### Project Description

Controlling phase separation processes in material science allows to influence the quality, functionality or life time expectancy of materials. Utilizing a phase field approach coupled with relevant physical phenomena such as either the Navier-Stokes system or the Navier-Lame system the project work aims at deriving first and second order optimality characterizations for the associated optimal control problems and efficient numerical solution algorithms relying on adaptive discretization and Newton-type solvers. The derivation of optimality conditions is challenged by the nature of the free energy involved in the phase field model, and the solver design has to cope with potentially involved non-differentiabilities and the large scale of the discretized systems.Project Website at MATHEON

##### People

**Head:**Prof. Michael Hintermüller (e-mail)**Ph.D. student:**Simon Rösel (e-mail)**PostDoc:**Donat Wegner (e-mail)**Assistants:**Thomas Surowiec (e-mail), Andrea von Schirp (e-mail)

##### Project related publications

Authors | Title | Journal |
---|---|---|

M. Hintermüller, R.H.W. Hoppe |
Goal-oriented adaptivity in control constrained optimal control of partial differential equations | SIAM Journal on Control and Optimization, 47 (2008), pp. 1721-1743 |

M. Hintermüller, I. Kopacka |
Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm | SIAM J. Optim. Volume 20, Issue 2, pp. 868-902 (2009) |

M. Hintermüller, K. Kunisch |
PDE-Constrained Optimization Subject to Pointwise Constraints on the Control, the State and its Derivative | SIAM J. Optim., Vol. 20, Issue 3, pp. 1133-1156 (2009) |

M. Hintermüller, M. Hinze |
Moreau-Yosida Regularization in State Constrained Elliptic Control Problems: Error Estimates and Parameter Adjustment | SIAM J. on Numerical Analysis, Volume 47, Issue 3, pp. 1666-1683 (2009) |

M. Hintermüller, I. Kopacka |
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs | Computational Optimization and Applications, Volume 50, Number 1, pp. 111-145 |

M. Hintermüller, V. Kovtunenko, K. Kunisch |
Obstacle problems with cohesion: a hemivariational inequality approach and its efficient numerical solution | SIAM Journal on Optimization 21 (2), 2011, pp. 491-516 |

M. Hintermüller, M. Hinze, M.H. Tber |
An Adaptive Finite Element Moreau-Yosida-Based Solver for a Non-smooth Cahn-Hilliard Problem | SIAM Journal on Control and Optimization 48 (7), 2011, pp. 4419-4452 |

M. Hintermüller, V. Kovtunenko |
From Shape Variation to Topology Changes in Constrained Minimization: A Velocity Method-Based Concept | Optimization Methods and Software 26 (4-5), 2011, pp. 513-532 |

J.-C. de los Reyes, M. Hintermüller |
A duality based semismooth Newton framework for solving variational inequalities of the second kind | Interfaces and Free Boundaries 13 (4), 2011, pp. 437-462 |

M. Hintermüller, T. Surowiec |
First Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis | SIAM Journal on Optimization 21 (4), 2011, pp. 1561-1593 |

M. Hintermüller, D. Wegner |
Distributed optimal control of the Cahn-Hilliard system including the case of a double-obstacle homogeneous free energy density | SIAM Journal on Control and Optimization 51 (1), 2012, pp. 388-418 |

M. Hintermüller, B.S. Mordukhovich, T. Surowiec |
Several Approaches for the Derivation of Stationarity Conditions for Elliptic MPECs with Upper-Level Control Constraints | MATHEON-Preprint No. 877 |

M. Hintermüller, M. Hinze, C. Kahle |
An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system | MATHEON-Preprint No. 908 |

M. Hintermüller, B.S. Mordukhovich, T. Surowiec |
Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints | IFB-Report No. 46 (07/2011), Institute of Mathematics and Scientific Computing, University of Graz |

M. Hintermüller, D. Wegner |
Optimal control of a semidiscrete Cahn-Hilliard-Navier-Stokes system | IFB-Report No. 53 (01/2012), Institute of Mathematics and Scientific Computing, University of Graz |

M. Hintermüller, T. Surowiec |
A PDE-constrained generalized Nash equilibrium problem with pointwise control and state constraints | IFB-Report No. 56 (03/2012), Institute of Mathematics and Scientific Computing, University of Graz |

M. Hintermüller, R.H.W. Hoppe, C. Löbhard |
A dual-weighted residual approach to goal-oriented adaptivity for optimal control of elliptic variational inequalities | IFB-Report No. 63 (11/2012), Institute of Mathematics and Scientific Computing, University of Graz |

M. Hintermüller, T. Surowiec |
A Bundle-Free Implicit Programming Approach for a Class of MPECs in Function Space | IFB-Report No. 60 (09/2012), Institute of Mathematics and Scientific Computing, University of Graz |

M. Hintermüller, S. Rösel |
A duality-based path-following semismooth Newton method for elasto-plastic contact problems | IFB-Report No. 70 (09/2013), Institute of Mathematics and Scientific Computing, University of Graz |