```markdown
### Image Description

The image contains a mathematical example and a graph related to convex optimization.

#### Mathematical Expression
- The function \( f(x) \) is defined as:
  \[
  f(x) = -\sum_{i=1}^{10000} \log(1 - x_i^2) - \sum_{i=1}^{100000} \log(b_i - a_i^T x)
  \]
- The example is set in \( \mathbb{R}^{10000} \) with sparse \( a_i \).

#### Graph
- The graph plots \( f(x^{(k)}) - p^* \) against \( k \).
- The x-axis is labeled \( k \) and ranges from 0 to 20.
- The y-axis is labeled \( f(x^{(k)}) - p^* \) and ranges from \( 10^{-5} \) to \( 10^5 \).
- Data points are marked with circles and show a decreasing trend.

#### Additional Information
- Backtracking parameters are \( \alpha = 0.01 \), \( \beta = 0.5 \).
- Performance is noted to be similar to small examples.

#### Source
- A. d’Aspremont. Convex Optimization M2. Slide 25/53.
```