  We present a numerical method for the local solution of nonlinear programming
problems. The SUMT approach of Fiacco and McCormick results in a merit function
with quadratic penalties and logarithmic barriers. Our NLP solver works by
directly minimizing this merit function.
  In our method, we use different concepts that each shall aim at the efficient
treatment of one respective special feature of this merit function. The
features are: large quadratic penalty terms, and badly scaled logarithmic
barriers.
  The quadratic penalties are treated with a modified Augmented Lagrangian
technique. It enables large step sizes despite nonlinearity of the equality
constraints. The logarithmic barriers we treat with a primal-dual
interior-point path-following technique.
  We prove global convergence of the method and local quadratic convergence. We
further prove weak polynomial time-complexity in the special case where the
nonlinear program is a linear program.
  We also use a trust-funnel so to avoid that the method converges to any
stationary points that are infeasible to the constraints.
