```markdown
### Second-order Cone Programming

**Objective:**
- Minimize \( f^T x \)

**Subject to:**
- \( \|A_i x + b_i\|_2 \leq c_i^T x + d_i, \quad i = 1, \ldots, m \)
- \( Fx = g \)

**Parameters:**
- \( A_i \in \mathbb{R}^{n_i \times n}, \quad F \in \mathbb{R}^{p \times n} \)

**Notes:**
- Inequalities are called second-order cone (SOC) constraints.
- \( (A_i x + b_i, c_i^T x + d_i) \) is in a second-order cone in \( \mathbb{R}^{n_i + 1} \).
- For \( n_i = 0 \), problem reduces to a linear program (LP).
- If \( c_i = 0 \), problem reduces to a quadratically constrained quadratic program (QCQP).
- More general than QCQP and LP.

**Reference:**
- A. d’Aspremont. Convex Optimization M2.
```
