```markdown
### Image Description

The image is a slide from a presentation on convex optimization. It includes a numerical example involving 150 randomly generated instances of an optimization problem. The problem is to minimize the function:

\[ f(x) = -\sum_{i=1}^{m} \log(b_i - a_i^T x) \]

#### Plot Details

- **Axes:**
  - X-axis: \( f(x^{(0)}) - p^\star \)
  - Y-axis: iterations

- **Data Points:**
  - Circles (\(\bigcirc\)): \( m = 100, n = 50 \)
  - Squares (\(\square\)): \( m = 1000, n = 500 \)
  - Diamonds (\(\diamond\)): \( m = 1000, n = 50 \)

#### Observations

- The plot shows the relationship between the initial function value difference \( f(x^{(0)}) - p^\star \) and the number of iterations required for convergence.
- The number of iterations is generally smaller than the bound \( 375(f(x^{(0)}) - p^\star) + 6 \).
- A bound of the form \( c(f(x^{(0)}) - p^\star) + 6 \) with a smaller \( c \) is empirically valid.

#### Additional Information

- The slide is from a presentation by A. d'Aspremont on convex optimization, specifically slide 30 out of 53.
```
