```markdown
## Matrix Norm Minimization

### Objective
Minimize the matrix 2-norm:
\[
\|A(x)\|_2 = \left(\lambda_{\max}(A(x)^T A(x))\right)^{1/2}
\]

### Matrix Definition
Where \( A(x) = A_0 + x_1 A_1 + \cdots + x_n A_n \) with given \( A_i \in S^{p \times q} \).

### Equivalent Semidefinite Program (SDP)
Minimize:
\[
t
\]

Subject to:
\[
\begin{bmatrix}
tI & A(x) \\
A(x)^T & tI
\end{bmatrix} \succeq 0
\]

### Variables
- \( x \in \mathbb{R}^n \)
- \( t \in \mathbb{R} \)

### Constraint Justification
The constraint follows from:
\[
\|A\|_2 \leq t \iff A^T A \preceq t^2 I, \quad t \geq 0
\]
\[
\iff \begin{bmatrix}
tI & A \\
A^T & tI
\end{bmatrix} \succeq 0
\]

*Source: A. d'Aspremont. Convex Optimization M2.*
```
