The TPS92512 datasheet clearly states a minimum Vin of 4.5V, but also an undervoltage lockout of only 2.94V. So - what happens if I attempt to use the part with Vin = 3.5V? I only have one LED, with a Vf around 2.9V, so there's enough headroom otherwise. I know that the TPS92510 is rated down to 3.5V, but I really like the Iadj feature of the TPS92512.