We propose an interior-point algorithm based on an elastic formulation of the L1-penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban and Toint (2003) and naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Remarkably, the method allows for a unified treatment of both general, unstructured, and structured degenerate problems, such as problems with complementarity constraints, with no changes to accommodate one class or the other. Numerical results on a standard test set illustrate the efficiency and robustness of the approach.
Cahier du Gerad G-2009-74, GERAD, HEC Montréal 3000, chemin de la Côte-Sainte-Catherine Montréal (Québec) Canada H3T 2A7, 11/2009