Optimization and Systems Theory Seminar
Tuesday, September 25, 2001, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Sven Leyffer
Department of Mathematics
University of Dundee
Dundee, Scotland, UK
E-mail: sleyffer@maths.dundee.ac.uk

How the Grinch solved MPECs, mathematical programs with equilibrium constraints

Equilibrium constraints in the form of complementarity conditions, and more generally variational inequalities, often appear as constraints in optimization problems. Applications of equilibrium constraints are widespread and fast growing. They cover very diverse areas such as the design of structures involving friction, elasto-hydrodynamic lubrication, taxation models, the modeling of competition in deregulated electricity markets and transportation network design.

Over recent years, it has become evident that equilibrium constraints cannot be solved satisfactorily with standard techniques for Nonlinear Programming (NLP). Both numerical and theoretical evidence has been advanced which support this view.

This talk is aimed at a general mathematical audience and starts by introducing and reviewing equilibrium constraints. We then give some applications which emphasize the usefulness and elegance of equilibrium constraints as a modeling tool.

Next, the assertion that standard techniques for NLP cannot be applied to equilibrium constraints is re-examined and some startling numerical evidence is presented using our own NLP solver.

The talk concludes by examining the local convergence properties of certain NLP methods applied to MPECs. It is shown that a simple constraint relaxation strategy allows a proof of second order convergence to be given under reasonable assumptions. A number of illustrative examples are presented which show that some of the assumptions are difficult to relax.

Calendar of seminars
Last update: September 14, 2001 by Anders Forsgren, anders.forsgren@math.kth.se.