The Penalty Interior-Point Method Fails to Converge

TitleThe Penalty Interior-Point Method Fails to Converge
Publication TypeReport
Year of Publication2003
AuthorsLeyffer, S
Date Published09/2003
Other NumbersANL/MCS-P1091-0903

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.