  Semi-infinite programming can be used to model a large variety of complex
optimization problems. The simple description of such problems comes at a
price: semi-infinite problems are often harder to solve than finite nonlinear
problems. In this paper we combine a classical adaptive discretization method
developed by Blankenship and Falk and techniques regarding a semi-infinite
optimization problem as a bi-level optimization problem. We develop a new
adaptive discretization method which combines the advantages of both techniques
and exhibits a quadratic rate of convergence. We further show that a limit of
the iterates is a stationary point, if the iterates are stationary points of
the approximate problems.
