This is an announcement for the paper "Perturbation of farthest points in weakly compact sets" by Jean-Matthieu Auge. Abstract: If $f$ is a real valued weakly lower semi-continous function on a Banach space $X$ and $C$ a weakly compact subset of $X$, we show that the set of $x \in X$ such that $z \mapsto \|x-z\|-f(z)$ attains its supremum on $C$ is dense in $X$. We also construct a counter example showing that the set of $x \in X$ such that $z \mapsto \|x-z\|+\|z\|$ attains its supremum on $C$ is not always dense in $X$. Archive classification: math.FA Mathematics Subject Classification: Primary 41A65 Remarks: 5 pages Submitted from: jean-matthieu.auge@math.u-bordeaux1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.2047 or http://arXiv.org/abs/1204.2047