  This paper presents a new linear hyperspectral unmixing method of the minimum
volume class, termed \emph{simplex identification via split augmented
Lagrangian} (SISAL). Following Craig's seminal ideas, hyperspectral linear
unmixing amounts to finding the minimum volume simplex containing the
hyperspectral vectors. This is a nonconvex optimization problem with convex
constraints. In the proposed approach, the positivity constraints, forcing the
spectral vectors to belong to the convex hull of the endmember signatures, are
replaced by soft constraints. The obtained problem is solved by a sequence of
augmented Lagrangian optimizations. The resulting algorithm is very fast and
able so solve problems far beyond the reach of the current state-of-the art
algorithms. The effectiveness of SISAL is illustrated with simulated data.
