What is the optimal battery charging speed?
Lithium Ion batteries have an upper charge limit of 1C. This means once its capacity, or in your case 4000mA.

This does not mean that is the best, though. It is good to keep a margin. But the margin doesn't have to be large, as healthy cells of the LiIon type do not have a chemical recombination and produce nearly no heat while charging at an appropriate current.

Usually I take 0.5C, or in your case 2000mA. It'll get the job done in about 2 hours and your cell suffer nearly as little as when you charge it with 400mA or less.

Of course, if you want to squeeze ten more charge/discharge cycles out of it, you can limit your charging and discharging to 1/20th C, i.e. 200mA and your battery will love you for a few days more.

Other than that there's some guidelines to the best charging curves (which are a bit more complex than what a PSU does limited to current and peak voltage), but they will again only add a few percent at best to the lifetime.
The best advise is, charge them to 4.2V or even 4.15V instead of 4.25V or more and don't keep them connected to the power too long after they are full and to never discharge them below 10%, or more conservatively 20%. Or put in a voltage: Shut off at about 2.85V instead of 2.55V