```markdown
## Outline

- **Lagrange dual problem**
- **Weak and strong duality**
- **Geometric interpretation**
- **Optimality conditions**
- **Perturbation and sensitivity analysis**
- **Examples**
- **Theorems of alternatives**
- **Generalized inequalities**

*Source: A. d'Aspremont. Convex Optimization M2. Page 4/49*
```