```markdown
### Geometric Interpretation

This image provides a geometric interpretation of the dual function in the context of convex optimization with one constraint \( f_1(x) \leq 0 \).

**Key Elements:**

- **Dual Function Definition:**
  \[
  g(\lambda) = \inf_{(u,t) \in \mathcal{G}} (t + \lambda u), \quad \text{where} \quad \mathcal{G} = \{(f_1(x), f_0(x)) \mid x \in \mathcal{D}\}
  \]

- **Graphical Representation:**
  - The set \(\mathcal{G}\) is depicted as a shaded region in the \(u\)-\(t\) plane.
  - A line representing \(\lambda u + t = g(\lambda)\) acts as a (non-vertical) supporting hyperplane to \(\mathcal{G}\).
  - The hyperplane intersects the \(t\)-axis at \(t = g(\lambda)\).

- **Points:**
  - \(p^*\) and \(d^*\) are marked within the region \(\mathcal{G}\).

**Additional Notes:**

- The image includes two side-by-side plots illustrating these concepts.
- Annotations emphasize the role of the supporting hyperplane and its intersection with the \(t\)-axis.

**Source:**
A. d’Aspremont. Convex Optimization M2. Slide 18/49.
```
