Is this a convex function in $X$, where all the entries are real and $Y,\beta$ are constants where $X,Y$ are rectangular matrices and $\beta$ is a constant vector and $A,B$ are constant p.s.d matrices:
$ (Y-X\beta)(Y-X\beta)^T +Tr(X^TAX) - Tr(X^TBX)$
I know that the first two terms are convex and the third term with the negative sign included becomes a concave function, but what about the convexity of the sum of the three terms, i.e the convexity of the sum of first two terms (convex part) + the third term (concave part)?