Some Algorithms Arising in the Proof of the Kepler Conjecture

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 paper gives a series of nonlinear optimization algorithms and shows how a systematic application of these algorithms would bring substantial simplifications to the original proof.