This is an announcement for the paper "A useful lemma for Lagrange multiplier rules in infinite dimension" by Mohammed Bachir and Joel Blot. Abstract: We give some reasonable and usable conditions on a sequence of norm one in a dual banach space under which the sequence does not converges to the origin in the $w^*$-topology. These requirements help to ensure that the Lagrange multipliers are nontrivial, when we are interested for example on the infinite dimensional infinite-horizon Pontryagin Principles for discrete-time problems. Archive classification: math.FA Submitted from: mohammed.bachir@univ-paris1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1507.01919 or http://arXiv.org/abs/1507.01919