##### Project Title

** Elliptic Mathematical Programs with Equilibrium Constraints (MPECs) in function space:
optimality conditions and numerical realization. **

##### People

**Head:**Prof. Michael Hintermüller [e-mail]**Researchers:**Dr. Thomas Surowiec [e-mail], Dr. Antoine Laurain [e-mail]

##### Project Description [detailed summary]

Schematic of Inexact

Path-Following

The project work concentrates on the development of a suitable optimality theory as well as the design and implementation of efficient solution algorithms for classes of MPECs in function space which are governed by elliptic (quasi)variational inequalities. Among others, the results will be applied to the following processes:

Bingham-Fluid

in a Pipe

- Stationary magnetization of type-II superconductors;
- Control of torsion phenomena with variable plasticity threshold;
- Ionization problems in electrostatics.

Results of Descent Algorithm

Since discretized MPECs result in large scale problems, tailored numerical solution techniques relying on adaptive finite element methods, semismooth Newton and multilevel techniques are developed within this project. The semi- or non-smoothness aspect arises due to the equivalence of the first order optimality systems to non-smooth operator equations.

[project website] at DFG##### Guests

- M. Hassan Farshbaf-Shaker (U. Regensburg)
- Juan Carlos de los Reyes (EPN Quito)
- Alexandra Gaevskaya (U. Augsburg)
- Arnaud Munch (U. Clermont-Ferrand)
- Samuel Amstutz (U. Avignon)
- Boris Mordukhovich (Wayne State U.)

##### Project Related Publications

Author | Title | Journal / Publisher | Bibtex |
---|---|---|---|

M. Hintermüller, T. Surowiec |
First Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis | To Appear in SIAM J. Opt. 2011 | |

M. Hintermüller, V. Kovtunenko, K. Kunisch |
Obstacle Problems with Cohesion: A Hemi-Variational Inequality Approach and its Efficient Numerical Solution. | SIAM Journal on Optimization 21 (2), 2011, pp. 491-516 | [bib] |

M. Hintermüller, A. Laurain |
Optimal shape design subject to elliptic variational inequalities | SIAM Journal on Control and Optimization, Vol.49 (2011), No.3, pp. 1015-1047 | [bib] |

M. Hintermüller, I. Kopacka |
A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs. | Computational Optimization and
Applications. DOI: 10.1007/s10589-009-9307-9 (2009) |
[bib] |

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) |
[bib] |

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) | [bib] |

##### Preprints

Author | Title |
---|---|

M. Hintermüller, B.S. Mordukhovich, T. Surowiec |
Several Approaches for the Derivation of Stationarity Conditions for Elliptic MPECs with Upper-Level Control Constraints |

M. Hintermüller, C.N. Rautenberg |
A Sequential Minimization Technique for Elliptic Quasi-Variational Inequalities with Gradient Constraints |

M. Freiberger, M. Hintermueller, A. Laurain, H. Scharfetter |
Topological sensitivity analysis in fluorescence optical tomography |

C. Conca, A. Laurain, R. Mahadevan |
Minimization of the ground state for two phase conductors in low contrast regime |

M. Hintermüller, C.Y. Kao, A. Laurain |
Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions |

M. Hintermüller, J.C. de los Reyes |
A Duality-Based Semismooth Newton Framework for Solving Variational Inequalities of the Second Kind. |