```markdown
### Image Description

The image is a slide from a presentation on convex optimization, specifically discussing the concept of epigraph variation and strong duality.

#### Epigraph Variation
- The slide introduces a set \( \mathcal{A} = \{(u, t) \mid f_1(x) \leq u, f_0(x) \leq t \text{ for some } x \in \mathcal{D}\} \).
- A graph is shown with axes labeled \( u \) and \( t \). The region \( \mathcal{A} \) is shaded.
- A curve within the shaded region represents the boundary of \( \mathcal{A} \).
- A point \( p^\star \) is marked on the graph.
- A line labeled \( \lambda u + t = g(\lambda) \) intersects the graph, with \( g(\lambda) \) marked on the \( u \)-axis.

#### Strong Duality
- The slide states conditions for strong duality:
  - It holds if there is a non-vertical supporting hyperplane to \( \mathcal{A} \) at \( (0, p^\star) \).
  - For convex problems, \( \mathcal{A} \) is convex and has a supporting hyperplane at \( (0, p^\star) \).
  - Slater’s condition: If there exist \( (\tilde{u}, \tilde{t}) \in \mathcal{A} \) with \( \tilde{u} < 0 \), then supporting hyperplanes at \( (0, p^\star) \) must be non-vertical.

#### Additional Information
- The slide is from a presentation by A. d’Aspremont on Convex Optimization M2, page 19/49.
```
