We propose an interior-point algorithm based on an elastic formulation of the
\(\ell_1\)-penalty merit function for mathematical programs with complementarity constraints.
The salient feature of our method is
that it requires no prior knowledge of which constraints, if any, are complementarity constraints. Remarkably, the method allows for a unied treatment of both general, unstructured, degenerate problems
and structured degenerate problems, such as problems with complementarity constraints, with no changes
to accommodate one class or the other. Our results refine those of Gould et al. (2010) by isolating the
degeneracy due to the complementarity constraints. The method naturally converges to a strongly stationary point or delivers a relevant certificate of degeneracy without recourse to second-order intermediate
solutions. Preliminary numerical results on a standard test set illustrate the
flexibility of the approach.
Published November 2009 , 27 pages
This cahier was revised in September 2011