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How to use Nearest inside Minimize?

The following returns errors but if # - {a, b} is replaced with # - {1, 2} it works correctly so I guess the errors are due to Nearest not returning numeric outputs.

x = RandomInteger[{-10, 10}, {10, 2}]
y = RandomInteger[{-10, 10}, {10, 2}]
Minimize[(# - Nearest[y, #][[1]] & /@ (# - {a, b} & /@ x))^2 // 
   Flatten // Total, {a, b}]
Clear[x, y]
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  • $\begingroup$ I recommend using nf = Nearest[...data...] outside the Minimize first, then using the nf inside the minimize for performance reasons, to avoid repeatedly calculating the acceleration structure while doing the minimization. $\endgroup$
    – flinty
    Commented Oct 16, 2023 at 11:03

1 Answer 1

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  • Use the ?NumericQ skill.
SeedRandom[1];
x = RandomInteger[{-10, 10}, {10, 2}];
y = RandomInteger[{-10, 10}, {10, 2}]; 
f[a_?NumericQ, 
  b_?NumericQ] := (# - Nearest[y, #][[1]] & /@ (# - {a, b} & /@ 
        x))^2 // Flatten // Total;
 NMinimize[f[a, b], {a, b}]

{83.7, {a -> 0.3, b -> -0.8}}

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