On LICQ and the uniqueness of Lagrange multipliers

On LICQ and the uniqueness of Lagrange multipliers

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Article ID: iaor2013735
Volume: 41
Issue: 1
Start Page Number: 78
End Page Number: 80
Publication Date: Jan 2013
Journal: Operations Research Letters
Authors:
Keywords: lagrange multipliers
Abstract:

Kyparisis proved in 1985 that a strict version of the Mangasarian–Fromovitz constraint qualification (MFCQ) is equivalent to the uniqueness of Lagrange multipliers. However, the definition of this strict version of MFCQ requires the existence of a Lagrange multiplier and is not a constraint qualification (CQ) itself. In this note we show that LICQ is the weakest CQ which ensures the (existence and) uniqueness of Lagrange multipliers. We also recall the relations between other CQs and properties of the set of Lagrange multipliers.

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