  Simple derivations, at a level appropriate for an undergraduate computational
physics course, of the most popular methods for finding the minimum of a
function of many variables are presented in a unified manner in the context of
a general optimization scheme that emphasizes their essential similarities. The
derivations in this paper encompass the conjugate gradient methods with and
without conditioning, and the variable metric methods. The common variants of
these methods including Fletcher-Reeves, Polak-Ribiere,
Davidon-Fletcher-Powell, and Broyden-Fletcher-Goldfarb-Shanno are described and
motivated.
