%0 Journal Article
%T Penalty Interior-Point Method Fails to Converge
%A Sven Leyffer
%J Mathematics
%D 2003
%I arXiv
%X Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A popular method for solving MPCCs is the penalty interior-point algorithm (PIPA). This paper presents a small example for which PIPA converges to a nonstationary point, providing a counterexample to the established theory. The reasons for this adverse behavior are discussed.
%U http://arxiv.org/abs/math/0310357v1