Optimization function convex or not

Question

I need to comment whether my optimization function is convex or non-convex. My optimization function is in the form of $(y-y_{cap})^2$. y is know. $y_{cap}$ comes out of a MATLAB pfile. So, $y_{cap}$ can be considered output of a black-box model. It is also not possible to plot $y-y_{cap}$ as it is a $22\times8$ matrix. Please help me to comment whether the optimization function is convex or non-convex,

Answer 1

I assume that you have a black-box model, which takes some inputs $x$ and map them to $y_{cap}$. Lets call this model $B$, so we have $y_{cap} = B(x)$. Then, your objective is $$\|y - B(x)\|^2.$$ This is not convex, unless $B$ is actually an affine function.