Lisa C. Hegerhorst-Schultchen ; Christian Kirches ; Marc C. Steinbach - Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

jnsao:6673 - Journal of Nonsmooth Analysis and Optimization, February 18, 2021, Volume 2 - https://doi.org/10.46298/jnsao-2021-6673
Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

Authors: Lisa C. Hegerhorst-Schultchen ; Christian Kirches ; Marc C. Steinbach

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 prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.


Volume: Volume 2
Section: Original research articles
Published on: February 18, 2021
Submitted on: July 30, 2020
Keywords: Mathematics - Optimization and Control,90C30, 90C33, 90C46


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