This paper focuses on solving mathematical programs with complementarity constraints (MPCCs) without assuming MPCC-LICQ or lower level strict complementarity at a solution. We show that a local minimizer of an MPCC is “piecewise M-stationary” un- der MPCC-GCQ; furthermore, every weakly stationary point of an MPCC is B-stationary if MPCC-ACQ holds. For the Bounding Algorithm proposed … Read more
This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie’s and Guignard’s kink qualification and … Read more
This work is part of an ongoing effort of comparing non-smooth optimization problems in abs-normal form to MPCCs. We study the general abs-normal NLP with equality and inequality constraints in relation to an equivalent MPCC reformulation. We show that kink qualifications and MPCC constraint qualifications of linear independence type and Mangasarian-Fromovitz type are equivalent. Then … Read more