  We optimize a collision-induced cooling process for ultracold atoms in the
nondegenerate regime. It makes use of a Feshbach resonance, instead of rf
radiation in evaporative cooling, to selectively expel hot atoms from a trap.
Using functional minimization we analytically show that for the optimal cooling
process the resonance energy must be tuned such that it linearly follows the
temperature. Here, optimal cooling is defined as maximizing the phase-space
density after a fixed cooling duration. The analytical results are confirmed by
numerical Monte-Carlo simulations. In order to simulate more realistic
experimental conditions, we show that background losses do not change our
conclusions, while additional non-resonant two-body losses make a lower initial
resonance energy with non-linear dependence on temperature preferable.
