```markdown
### Image Description

The image illustrates the concept of "choice of norm for steepest descent" in optimization. It consists of two diagrams, each showing a sequence of points connected by arrows, representing steps in the steepest descent method. The diagrams are overlaid with ellipses that represent level sets of quadratic norms.

- **Left Diagram:**
  - Points labeled \( x^{(0)} \), \( x^{(1)} \), and \( x^{(2)} \).
  - Ellipses indicate level sets \( \{ x \mid \| x - x^{(k)} \|_P = 1 \} \).

- **Right Diagram:**
  - Points labeled \( x^{(0)} \), \( x^{(1)} \), and \( x^{(2)} \) with a denser sequence of steps.
  - Similar ellipse level sets as the left diagram.

### Annotations

- **Text:**
  - "steepest descent with backtracking line search for two quadratic norms"
  - "ellipses show \( \{ x \mid \| x - x^{(k)} \|_P = 1 \} \)"
  - "equivalent interpretation of steepest descent with quadratic norm \( \| \cdot \|_P \): gradient descent after change of variables \( \tilde{x} = P^{1/2} x \)"
  - "shows choice of \( P \) has strong effect on speed of convergence"

- **Footer:**
  - "A. d'Aspremont. Convex Optimization M2." 
  - Page number "15/53"

The image emphasizes how the choice of norm \( P \) affects the convergence speed of the steepest descent algorithm.
```