Abstract:
Mathematical Programs with Equilibrium Constraints (MPECs) occur in
many practical applications ranging from the optimal control of contact
phenomena or phase separation in materials to parameter identification
in elasto-hydrodynamic lubrication problems or to calibration problems
in mathematical finance. These problems typically involve variational
inequality constraints describing the underlying state system and turn
out to be significantly less researched then MPECs in finite dimensions.
From an optimization theoretic point of view the pertinent minimization
problems are generically degenerate and first order optimality cannot be
obtained from well-established Karush-Kuhn-Tucker-type theory in Banach
spaces.
In this talk, due to the constraints degeneracy and the utilized analytical tools several notions of stationarity for MPECs in function space are introduced. The latter notions are reminiscences of corresponding finite dimensional concepts such as weak-, C-, or S-stationarity. Based on the proof technique to obtain first order optimality, path-following-type solution algorithms are introduced and a report on their numerical performance is given. Also a brief report on nonlinear multigrid approaches to problems with so-called upper level constraints is given. While the aforementioned numerical tests are primarily for elliptic MPECs, at the end of the presentation some theoretical and numerical challenges in the context of parabolic MPECs are discussed as well.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.