How Stringent Is the Linear Independence Assumption for Mathematical Programs with Complementarity Constraints?

The linear independence constraint qualifications (LICQ) plays an important role in the analysis of mathematical programs with complementarity constraints (MPCCs) and is a vital ingredient to convergence analyses of SQP-type or smoothing methods, cf., e.g., Fukushima and Pang (1999), Luo et al. (199...

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Bibliographic Details
Published in:Mathematics of operations research 2001-11, Vol.26 (4), p.851-863
Main Authors: Scholtes, Stefan, Stohr, Michael
Format: Article
Language:English
Subjects:
complementarity constraints
Constraint qualification
critical point
Critical points
Data smoothing
Index sets
Linear complementarity problem
Mathematical functions
Mathematical programming
Mathematical theorems
Mathematics
Nonlinear programming
Operations research
Studies
Topological spaces
Topological vector spaces
Topology
Variational inequalities
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Summary:The linear independence constraint qualifications (LICQ) plays an important role in the analysis of mathematical programs with complementarity constraints (MPCCs) and is a vital ingredient to convergence analyses of SQP-type or smoothing methods, cf., e.g., Fukushima and Pang (1999), Luo et al. (1996), Scholtes and Stöhr (1999), Scholtes (2001), Stöhr (2000). We will argue in this paper that LICQ is not a particularly stringent assumption for MPCCs. Our arguments are based on an extension of Jongen's (1977) genericity analysis to MPCCs. His definitions of nondegenerate critical points and regular programs extend naturally to MPCCs and his genericity results generalize straightforwardly to MPCCs in standard form. An extension is not as straightforward for MPCCs with the particular structure induced by lower-level stationarity conditions for variational inequalities or optimization problems. We show that LICQ remains a generic property for this class of MPCCs.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.26.4.851.10007