A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints
Computational Optimization and Applications
Newton-Type method for a class of mathematical programs with complementarity constraints
Computers & Mathematics with Applications
Computational Optimization and Applications
A Comparison of Electricity Market Designs in Networks
Operations Research
On Stability of the Feasible Set of a Mathematical Problem with Complementarity Problems
SIAM Journal on Optimization
The C-Index: A New Stability Concept for Quadratic Programs with Complementarity Constraints
Mathematics of Operations Research
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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 St脙露hr (1999), Scholtes (2001), St脙露hr (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.