it was shown in a 2008 paper by de silva and lim that the above standard approximation problem may be "ill-posed". a solution to aforementioned problem may sometimes not exist because the set over which one optimizes is not closed. as such, a minimizer may not exist, even though an infimum would exist. in particular, it is known that certain so-called "border tensors" may be approximated arbitrarily well by a sequence of tensor of rank at most formula_6, even though the limit of the sequence converges to a tensor of rank strictly higher than formula_6. the rank-3 tensor