```markdown
### Examples

#### Least-Squares

- **Objective:** Minimize \( \|Ax - b\|_2^2 \)
- **Solution:** Analytical solution \( x^\star = A^\dagger b \) where \( A^\dagger \) is the pseudo-inverse.
- **Constraints:** Can add linear constraints, e.g., \( l \preceq x \preceq u \).

#### Linear Program with Random Cost

- **Objective:** Minimize \( \bar{c}^T x + \gamma x^T \Sigma x = \mathbb{E} c^T x + \gamma \text{var}(c^T x) \)
- **Constraints:** Subject to \( Gx \preceq h, \ Ax = b \).

- **Details:**
  - \( c \) is a random vector with mean \( \bar{c} \) and covariance \( \Sigma \).
  - Therefore, \( c^T x \) is a random variable with mean \( \bar{c}^T x \) and variance \( x^T \Sigma x \).
  - \( \gamma > 0 \) is a risk aversion parameter; it controls the trade-off between expected cost and variance (risk).

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