Centre for Discrete and Applicable Mathematics
	CDAM Research Report, LSE-CDAM-2003-16 November 2003

Abstract

Liminal constraints are active inequality constraints with zero Lagrange multipliers. This is the borderline case between inactive and binding inequality constraints. In correctly formulated second-order conditions, inactive constraints are ignored, and binding ones are treated like equality constraints. But liminal constraints can neither be ignored nor be treated like equalities; examples are given. The persistent assertion in economics texts that all active constraints can be treated like equalities is untrue, and gives a false "sufficient" second-order condition.

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