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### Slater’s Constraint Qualification

**Convex problem:**

- **Objective:** Minimize \( f_0(x) \)
- **Subject to:**
  - \( f_i(x) \leq 0, \quad i = 1, \ldots, m \)
  - \( Ax = b \)

**Slater's Condition:**

The problem satisfies Slater's condition if it is **strictly feasible**, i.e.,

\[ \exists x \in \text{int} \mathcal{D} : f_i(x) < 0, \quad i = 1, \ldots, m, \quad Ax = b \]

- **Implications:**
  - Guarantees that the dual optimum is attained (if \( p^\star > -\infty \))
  - There exist many other types of constraint qualifications

*Source: A. d’Aspremont. Convex Optimization M2.*
```