Maximizing over a 1D region

Question

Why does the following not compute?

MaxValue[-y^2, y ∈ Interval[{-1, 1}]]

I expect it to compute the maximum value of the funtion over the interval from -1 to 1 but I instead get the error:

MaxValue::objfs: The objective function {-Subscript[y, 1]^2} should be scalar-valued.

What should I be using instead?

Answer 1

Update: Carl gave the best solution in a comment:

Could use {y} ∈ Interval[{-1, 1}] instead. – Carl Woll

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If you use the region notation, the variable is considered to be a vector. 1D region implies a 1D vector, but still a vector, not a scalar.

The following all work:

Explicitly take the first component of the vector. Since this is symbolic computation, we must use Indexed:

MaxValue[-Indexed[y, 1]^2, y ∈ Interval[{-1, 1}]]
(* 0 *)

Use a vector operator (Dot) to compute the same thing:

MaxValue[-y.y, y ∈ Interval[{-1, 1}]]
(* 0 *)

Instead of regions, use constraints:

MaxValue[{-y^2, -1 <= y <= 1}, y]
(* 0 *)