IFIP TC 7 / 2013 - Minisymposia

  • Gerd Wachsmuth, TU Chemnitz
"Optimal control of time-dependent variational inequalities"

Several physical phenomena can be modeled by time-dependent (and in particular rate-independent) variational inequalities. These processes include
  • hysteresis effects in plasticity or (ferro)-magnetics,
  • phase field models approximating moving interfaces and phase transitions, and
  • sweeping processes in the sense of Moreau.
Since the forward problem involves a variational inequality (or, after reformulation, a complementarity condition), the optimization of such processes yields infinite dimensional Mathematical Programs with
Equilibrium Constraints (MPECs) or Mathematical Programs with Complementarity Constraints (MPCCs).

It is well known that the structure of such optimization problems yields severe difficulties in the theoretical treatment as well as in numerical implementations.