```markdown
## Image Description

The image is a slide from a presentation on convex optimization. It is titled "Examples" and discusses an example in \( \mathbb{R}^2 \).

### Left Side
- **Contour Plot**: Shows a series of dashed ellipses representing level curves of a function in \( \mathbb{R}^2 \). 
- **Path**: A path is drawn with arrows indicating the trajectory from \( x^{(0)} \) to \( x^{(1)} \), suggesting an optimization process.

### Right Side
- **Graph**: A plot depicting the convergence of the function value \( f(x^{(k)}) - p^* \) on a logarithmic scale.
  - **Axes**: 
    - x-axis labeled \( k \), ranging from 0 to 5.
    - y-axis labeled \( f(x^{(k)}) - p^* \), ranging from \( 10^{-15} \) to \( 10^5 \).
  - **Data**: Points connected by a line, showing a decrease in function value over iterations.

### Notes
- **Backtracking Parameters**: \( \alpha = 0.1 \), \( \beta = 0.7 \).
- **Convergence**: The method converges in only 5 steps.
- **Quadratic Local Convergence**: Indicates rapid convergence near the solution.

### Footer
- **Source**: A. d’Aspremont. Convex Optimization M2.
- **Slide Number**: 23/53.
```
