[schiffern]

  >The rocket equation is what gives rise to the suicide burn being optimal

Nitpick, but this isn't strictly true.

Even if you don't count the vehicle getting lighter as it burns fuel (which is all the rocket equation does here), a suicide burn will still be optimal.

The real reason is because a suicide burn minimizes gravity loss.

https://en.wikipedia.org/wiki/Gravity_loss

[martincmartin]

OP here. True, I oversimplified. What I meant was, there are two parts to the dynamics, the rocket equation and gravity. They add linearly, so any extra velocity that comes from gravity needs to be eliminated by increasing the delta V from the rocket equation. The gravity delta V is just acceleration of gravity times time, so you want to minimize the time. Surprisingly (to me), in the rocket equation, it doesn't matter how long it takes, or what sequence of burns you use, or whether you burn at a constant rate all the way through vs short strong bursts, etc. So to land with zero velocity using the least fuel, you just need to land in the shortest amount of time.