  A quantum state's entanglement across a bipartite cut can be quantified with
entanglement entropy or, more generally, Schmidt norms. Using only Schmidt
decompositions, we present a simple iterative algorithm to maximize Schmidt
norms. Depending on the choice of norm, the optimizing states maximize or
minimize entanglement, possibly across several bipartite cuts at the same time
and possibly only among states in a specified subspace.
  Recognizing that convergence but not success is certain, we use the algorithm
to explore topics ranging from fermionic reduced density matrices and varieties
of pure quantum states to absolutely maximally entangled states and minimal
output entropy of channels.
