NONLINEAR PROGRAMMING METHODS FOR
OPTIMISATION PROBLEMS WITH COMPLEMENTARITY CONSTRAINTS

Nonlinear programs with complementarity constraints are becoming important in economics and engineering for both designing systems - e.g. setting tolls in a traffic network,or beam thickness in mechanical structures - and finding system parameters via inverse optimisation -
e.g. determining demand elasticities in American options pricing, or material properties in civil engineering.

While this class of problems can be tackled by classical nonlinear optimisation methods, it is also well known for apparently intrinsic theoretical and numerical difficulties.However, recent computational experiments initiated by Roger Fletcher and Sven Leyffer have shown surprisingly good behaviour of certain SQP-based methods, including superlinear convergence rates. We investigate this surprising phenomenon.