Complementarity constraints are a very versatile modeling tool,
widely used in important economics and engineering areas such as
robotics, virtual reality, structural engineering, chemical engineering,
data mining, homeland security, nuclear engineering, and network design.
Their most common occurrence is in game theoretical models and in
hierarchical optimization problems, where the lower-level problem has
inequality constraints. Applications involving complementarity constraints
span a broad spectrum of models that include contact between rigid or
elastic bodies; electricity, commodity or financial markets, and switches
in electrical networks. The talk will present recent advances in the
investigation of mathematical problems with complementarity constraints
and differential problems with complementarity constraints, and will
outline outstanding analytical, methodological and computational issues
that are of current interest to the optimization and applications communities.