Abstract

There is a link between two well-known constraint qualifications in nonlinear programming, namely, normality (implying a positive cost multiplier) and regularity (the tangent cone and the set of tangential constraints coincide): the former implies the latter. This fact has been crucial and a cornerstone for establishing second order conditions in terms of tangential constraints. For problems in the calculus of variations involving equality and inequality constraints, one can derive second order conditions in terms of the tangent cone and state a conjecture, based on tangential constraints, which is the counterpart of that in nonlinear programming. However, as we show in this paper, the link mentioned above between normality and regularity, in the infinite dimensional case, may fail to hold. (C) 2018 Elsevier B.V. All rights reserved.