  A numerical study of an optimal control formulation for a shape optimization
problem governed by an elliptic variational inequality is performed. The shape
optimization problem is reformulated as a boundary control problem in a fixed
domain. The discretized optimal control problem is a non-smooth and non-convex
mathematical programing problem. The performance of the standard BFGS
quasi-Newton method and the BFGS method with the inexact line search are
tested.
