I am reading a paper on using surrogate models to approximate multi-fidelity simulation optimisation problems and I can't quite understand what is meant by this notation they are using to construct the low-fidelity test function from the high-fidelity one.
They are using the standard Colville test function for the high-fidelity function, which has 4 real valued input variables $x_1 \in [-1,1]$ with $i = 1,2,3,4$ and a real valued correlation parameter $A \in [0,1]$. The function is given as follows:
$$y_h = 100(x_1^2 -x_2)^2 + (x_1-1)^2 + (x_3-1)^2 + 90(x_3^2 - x_4) + 10.1((x_2 -1)^2) + (x_4-1)^2) + 19.8(x_2-1)(x_4-1)$$
They use this $y_h$ result to construct a low-fidelity test function in the following way:
$$y_l = y_h(A^2(x_1,x_2,x_3,x_4)) - (A+0.5)(5x_1^2 + 4x_2^2 + 3x_3^2 + x_4^2)$$
I am a bit confused as to what the term $y_h(A^2(x_1,x_2,x_3,x_4))$ means though, because $A$ is a scalar value and isn't defined as a function with arguments or anything. My intuitive interpretation is that the first term of $y_l$ is just $A^2y_h$, and I thought potentially it could be meant that those are the inputs to $y_h$. Though $y_h$ isn't really defined as a function either, and then you have the problem of the $A^2$ term before the arguments are given anyway.
The other way that I suppose it could be interpreted is that $A^2()$ is some function that multiplies its arguments by $A^2$ and the output of that is passed to $y_h$, i.e., $y_h(A^2(x_1,x_2,x_3,x_4)) = y_h(A^2x_1,A^2x_2,A^2x_3,A^2x_4))$ but that seems pretty weird too..
Is this just some notation that I have not seen before? or is it just confusingly expressed?