  A method for the reconstruction of the primordial density fluctuation field
is presented. Various previous approaches to this problem rendered {\it
non-unique} solutions. Here, it is demonstrated that the initial positions of
dark matter fluid elements, under the hypothesis that their displacement is the
gradient of a convex potential, can be reconstructed uniquely. In our approach,
the cosmological reconstruction problem is reformulated as an assignment
problem in optimisation theory. When tested against numerical simulations, our
scheme yields excellent reconstruction on scales larger than a few megaparsecs.
