```markdown
### Operations that Preserve Convexity

**Practical methods for establishing convexity of a function:**

1. **Verify definition** (often simplified by restricting to a line)
2. For twice differentiable functions, show \( \nabla^2 f(x) \succeq 0 \)
3. Show that \( f \) is obtained from simple convex functions by operations that preserve convexity:
   - Nonnegative weighted sum
   - Composition with affine function
   - Pointwise maximum and supremum
   - Composition
   - Minimization
   - Perspective

*Source: A. d'Aspremont. Convex Optimization M2. Slide 15/67*
```