```markdown
### Image Description

The image presents a mathematical optimization problem in \( \mathbb{R}^{100} \). The objective function is defined as:

\[ f(x) = c^T x - \sum_{i=1}^{500} \log(b_i - a_i^T x) \]

A plot is shown below the equation, with the y-axis labeled \( f(x^{(k)}) - p^* \) ranging from \( 10^{-4} \) to \( 10^4 \) on a logarithmic scale, and the x-axis labeled \( k \) ranging from 0 to 200.

Two lines are plotted:

- A dashed line labeled "exact l.s." (line search).
- A solid line labeled "backtracking l.s." (line search).

The text below the plot indicates "‘linear’ convergence, i.e., a straight line on a semilog plot."

The slide is attributed to A. d’Aspremont from the lecture "Convex Optimization M2" and is numbered 12/53.
```