### Sven Leyffer (University of Dundee)

#### Equilibrium constraints: much ado about nothing?

*Tuesday 7 March 2000 at 15.30, JCMB 5326*

##### Abstract

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 starts by introducing and reviewing equilibrium
constraints and gives some applications which emphasize the
usefulness and elegance of equilibrium constraints as a
modeling tool.

Next, we re-examine the assertion that standard techniques
for NLP cannot be applied to equilibrium constraints and
present some startling numerical evidence using our own NLP
solver. The ultimate aim of this on-going work is the
development of a robust solver for optimization problems
with equilibrium constraints.

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