```markdown
### Robust Linear Programming

The image discusses the concept of robust linear programming, focusing on handling uncertainty in optimization problems. It presents the following key points:

- **Uncertainty in Parameters**: In linear programming (LP), parameters such as \( c \), \( a_i \), and \( b_i \) can be uncertain.

- **Optimization Problem**:
  - Objective: Minimize \( c^T x \)
  - Subject to constraints: \( a_i^T x \leq b_i \), for \( i = 1, \ldots, m \)

- **Approaches to Handling Uncertainty**:
  1. **Deterministic Model**:
     - Constraints must hold for all \( a_i \in \mathcal{E}_i \).
     - Formulation:
       - Minimize \( c^T x \)
       - Subject to \( a_i^T x \leq b_i \) for all \( a_i \in \mathcal{E}_i \), \( i = 1, \ldots, m \)

  2. **Stochastic Model**:
     - \( a_i \) is a random variable; constraints must hold with probability \( \eta \).
     - Formulation:
       - Minimize \( c^T x \)
       - Subject to \( \text{Prob}(a_i^T x \leq b_i) \geq \eta \), \( i = 1, \ldots, m \)

The slide is from a lecture by A. d'Aspremont on Convex Optimization.
```
