I am trying to figure out if it is possible to simplify the matrix expression for $M$ in terms of $x_i,y_i$:
$ M(x_i,y_i)=(A+\left[B_0+\sum_{i=1}^{m}B_i x_i\right])^{-1}(A-\left[B_0+\sum_{i=1}^{m}B_i y_i\right])$
Where $x_i,y_i \in \mathbb{R} $ are scalars, $ A=A^T \in \mathbb{R}^{n \times n} $ is a symmetric matrix and $B_i \in \mathbb{R}^{n \times n}$
A constraint of the form:
$ \boldsymbol v = M(x_i,y_i) \boldsymbol v_0 $
is a convex constraint?
Where $\boldsymbol v_0 \in \mathbb{R}^n$ is a given vector while $\boldsymbol v \in \mathbb{R}^{n}$
One way to rewrite the expression is as follows. Let $A^{1/2}$ denote the symmetric positive definite square root of $A$, and let $A^{-1/2}$ denote the inverse of $A^{1/2}$. Let $C_i = A^{-1/2}B_i A^{-1/2}$. We can write $$ M(x_i,y_i) = A^{-1/2}\left(I + C_0 + \left[\sum_{i=1}^{m}C_i x_i\right]\right)^{-1}\left(I-\left[C_0+\sum_{i=1}^{m}C_i y_i\right]\right)A^{1/2}. $$