```markdown
**Example:** Optimal allocation with resource constraint

Objective:
- **Minimize:** \( f_1(x_1) + f_2(x_2) + \cdots + f_n(x_n) \)
- **Subject to:** \( x_1 + x_2 + \cdots + x_n = b \)

**Eliminate** \( x_n = b - x_1 - \cdots - x_{n-1} \), i.e., choose

\[
\hat{x} = be_n, \quad F = \begin{bmatrix} I \\ -1^T \end{bmatrix} \in \mathbb{R}^{n \times (n-1)}
\]

**Reduced problem:**

- **Minimize:** \( f_1(x_1) + \cdots + f_{n-1}(x_{n-1}) + f_n(b - x_1 - \cdots - x_{n-1}) \)

(variables \( x_1, \ldots, x_{n-1} \))

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