```markdown
### Interpretation via KKT conditions

The image presents a slide discussing the interpretation of optimization solutions via KKT (Karush-Kuhn-Tucker) conditions. It outlines the following conditions:

1. **Primal constraints:** \( f_i(x) \leq 0, \, i = 1, \ldots, m, \, Ax = b \)
2. **Dual constraints:** \( \lambda \succeq 0 \)
3. **Approximate complementary slackness:** \(-\lambda_i f_i(x) = 1/t, \, i = 1, \ldots, m\)
4. **Gradient of Lagrangian with respect to \( x \) vanishes:**

   \[
   \nabla f_0(x) + \sum_{i=1}^{m} \lambda_i \nabla f_i(x) + A^T \nu = 0
   \]

The slide notes that the difference with standard KKT conditions is that condition 3 replaces \(\lambda_i f_i(x) = 0\).

The slide is attributed to A. d'Aspremont, from a course on Convex Optimization (M2).
```
