  Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI)
model fails to bring it to its ground state for a certain range of values of
the frustration parameter $\kappa$, the ratio of the next nearest neighbour
antiferromagnetic interaction strength to the nearest neighbour one. We apply
several annealing methods, both classical and quantum, and observe that the
behaviour of the residual energy and the order parameter depends on the value
of $\kappa$ strongly. Classical or thermal annealing is found to be adequate
for small values of $\kappa$.
  However, neither classical nor quantum annealing is effective at values of
$\kappa$ close to the fully frustrated point $\kappa=0.5$, where the residual
energy shows a very slow algebraic decay with the number of MCS.
