  The bilevel program is an optimization problem where the constraint involves
solutions to a parametric optimization problem. It is well-known that the value
function reformulation provides an equivalent single-level optimization problem
but it results in a nonsmooth optimization problem which never satisfies the
usual constraint qualification such as the Mangasarian-Fromovitz constraint
qualification (MFCQ). In this paper we show that even the first order
sufficient condition for metric subregularity (which is in general weaker than
MFCQ) fails at each feasible point of the bilevel program. We introduce the
concept of directional calmness condition and show that under {the} directional
calmness condition, the directional necessary optimality condition holds.
{While the directional optimality condition is in general sharper than the
non-directional one,} the directional calmness condition is in general weaker
than the classical calmness condition and hence is more likely to hold. {We
perform the directional sensitivity analysis of the value function and} propose
the directional quasi-normality as a sufficient condition for the directional
calmness. An example is given to show that the directional quasi-normality
condition may hold for the bilevel program.
