```markdown
### Inequality Form LP

#### Primal Problem
- **Objective:** Minimize \( c^T x \)
- **Subject to:** \( Ax \succeq b \)

#### Dual Function
- \( g(\lambda) = \inf_x ((c + A^T \lambda)^T x - b^T \lambda) = \)
  - \(-b^T \lambda\) if \( A^T \lambda + c = 0 \)
  - \(-\infty\) otherwise

#### Dual Problem
- **Objective:** Maximize \(-b^T \lambda\)
- **Subject to:** 
  - \( A^T \lambda + c = 0 \)
  - \( \lambda \succeq 0 \)

#### Notes
- From Slater's condition: \( p^* = d^* \) if \( Ax \prec b \) for some \( \tilde{x} \)
- In fact, \( p^* = d^* \) except when primal and dual are infeasible

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*Source: A. d’Aspremont. Convex Optimization M2. Slide 15/49.*
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