  By any account, the 1998 proof of the Kepler conjecture is complex. The
thesis underlying this article is that the proof is complex because it is
highly under-automated. Throughout that proof, manual procedures are used where
automated ones would have been better suited. This article gives a series of
nonlinear optimization algorithms and shows how a systematic application of
these algorithms would bring substantial simplifications to the original proof.
This article includes a discussion of quantifier elimination, linear assembly
problems, automated inequality proving, and plane graph generation in the
context of discrete geometry.
