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

Many phenomena in engineering, life sciences and mathematical finance of physics result in a mathematical model of variational or quasi-variational inequality type. Applications comprise contact problems (with friction) in elasticity, torsion problems in plasticity, option pricing in finance, the magnetization of superconductors or ionization problems in electrostatics. Often, one is interested in influencing the system under consideration by some control means in order to optimize a certain output quantity. The resulting optimization problem falls into the realm of Mathematical Programs with Equilibrium Constraints (MPECs), which are challenging due to constraint degenerary. 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: - Stationary magnetization of type-II superconductors; - Control of torsion phenomena with variable plasticity threshold; - Ionization problems in electrostatics.