Shimano Deore 2x10 derailleur M6025-L with 3x Alivio M4050 crank
Yes, it will work, but not optimally.
According to the bible:

"Double" front derailers will work with triples, but if the middle ring is much smaller than the big ring, they will be balky shifting up from the small to the middle chainring.

Several options:

Drop the smallest chainring. You won't need it anyway. I have done this and I'm happy with the result.
Learn proper front shifting technique and live with the poorer shifting of the double derailleur on a triple crankset.
Find a triple front derailleur.
Find a double crankset.

I used to have a very cheap bike with a double front derailleur and triple crankset. The diminished front shifting performance was not noticeable because all of the components were so poor that every shift was poor anyway, even in the rear!