On Constraint Qualifications for Mathematical Programs with Mixed Complementarity Constraints

2001 ◽  
pp. 253-271 ◽  
Author(s):  
J. V. Outrata
Keyword(s):  
Constraint Qualifications ◽  
Complementarity Constraints ◽  
Mathematical Programs

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

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.

A New Regularization Scheme for Mathematical Programs with Complementarity Constraints

2009 ◽  
Vol 20 (1) ◽  
pp. 78-103 ◽  
Author(s):  
Abdeslam Kadrani ◽  
Jean-Pierre Dussault ◽  
Abdelhamid Benchakroun
Keyword(s):  
Complementarity Constraints ◽  
Regularization Scheme ◽  
Mathematical Programs
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