```markdown
The image contains two plots comparing exact line search and backtracking line search methods in a convex optimization context in \( \mathbb{R}^{100} \).

**Left Plot:**
- **Title:** \( f(x^{(k)}) - p^* \) vs. \( k \)
- **Axes:**
  - x-axis: \( k \) (iteration number) ranging from 0 to 10.
  - y-axis: \( f(x^{(k)}) - p^* \) (objective function value difference) on a logarithmic scale from \( 10^{0} \) to \( 10^{-15} \).
- **Curves:** 
  - Two curves are shown: one labeled "exact line search" and the other "backtracking."
  - Both curves decrease over iterations, with the exact line search reaching lower values faster.

**Right Plot:**
- **Title:** Step size \( t^{(k)} \) vs. \( k \)
- **Axes:**
  - x-axis: \( k \) (iteration number) ranging from 0 to 8.
  - y-axis: Step size \( t^{(k)} \) ranging from 0 to 2.
- **Curves:**
  - Two curves are shown: one labeled "exact line search" and the other "backtracking."
  - The step size for exact line search shows more variability compared to backtracking.

**Annotations:**
- Backtracking parameters are \( \alpha = 0.01 \), \( \beta = 0.5 \).
- Backtracking line search is noted to be almost as fast as the exact line search and much simpler.
- The algorithm demonstrates two phases clearly.

**Source:** A. d'Aspremont. Convex Optimization M2. Page 24/53.
```
