```markdown
### Feasibility Problem

**Problem Statement:**

- **Find** \( x \)  
  **subject to**  
  \( f_i(x) \leq 0, \quad i = 1, \ldots, m \)  
  \( h_i(x) = 0, \quad i = 1, \ldots, p \)  

This can be considered a special case of the general problem with \( f_0(x) = 0 \):

- **Minimize** \( 0 \)  
  **subject to**  
  \( f_i(x) \leq 0, \quad i = 1, \ldots, m \)  
  \( h_i(x) = 0, \quad i = 1, \ldots, p \)  

**Outcomes:**

- \( p^\star = 0 \) if constraints are feasible; any feasible \( x \) is optimal.
- \( p^\star = \infty \) if constraints are infeasible.

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