For instance, if one wants to minimize a functional  formula_3  on the dual of a separable normed vector space "X", one common strategy is to first construct a minimizing sequence  formula_4  which approaches the infimum of "F", use the sequential Banach–Alaoglu theorem to extract a subsequence that converges in the weak* topology to a limit "x", and then establish that "x" is a minimizer of "F".