How to get Nearest lower value?

Question

Nearestgives me the closest value to my reference, but what if I am always looking for the closest value, which is lower than my reference?

list = {0.2, 0.25, 0.32, 0.36, 0.40, 0.45, 0.50, 0.55, 0.63, 0.70, 
0.80, 0.90, 1.00, 1.10, 1.25, 1.30, 1.40, 1.50, 1.60, 1.80, 2.00, 
2.20, 2.50, 2.80, 3.00, 3.20, 3.60, 4.00, 4.50, 5.00, 5.50, 6.30, 
7.00, 8.00};

ref = 3.902;

result = Nearest[list, ref][[1]]

4.

...as in the example above: how I tell Mathematica that I need the 3.6 value instead of 4.0?

Answer 1

Leave the elements greater than the reference out of consideration, by, for example, DeleteCases:

Nearest[DeleteCases[list, x_ /; x > ref], ref]

or Cases:

Nearest[Cases[list, x_ /; x < ref], ref]

or for any 1D list of numbers like in your case (I assume, list might also be unsorted)

Last@Sort@Select[list, # < ref &]

or simply replace Nearest with Max and apply to the list where numbers above ref have been dropped

Max@Select[list, # < ref &]

or several other ways which don't yet come to my mind.

Answer 2

Another possibility is to use a custom distance function with a penalty:

Nearest[list, 3.902, DistanceFunction -> (Abs[#1 - #2] + 100 Boole[#1 < #2] &)]
   {3.6}