Look for a LED driver.
You may need to revise your choice of power source depending on what you find.
If you do end up using a Li-Ion (LiPo, LiFe) battery, ensure the circuit will not over-discharge the battery. This is important for many battery types, but rather more critical for these.
The LM3410 seems to fit many of these requirements and looks like it will operate from a single cell. It does not appear to have an undervoltage shutdown, but I did not look in detail.
Also I noted that the max current is 2.8A for that device. You may not get a full 10W to your LED.
Ensure that your Li battery is capable of the current you require. Also ensure that your LED has a good heatsink. Both of these will help ensure a long lifetime for your device.