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### Duality and Problem Reformulations

- **Equivalent formulations** of a problem can lead to very different duals.
- **Reformulating the primal problem** can be useful when the dual is difficult to derive or uninteresting.

#### Common Reformulations

- Introduce new variables and equality constraints.
- Make explicit constraints implicit or vice-versa.
- Transform objective or constraint functions, e.g., replace \( f_0(x) \) by \( \phi(f_0(x)) \) with \( \phi \) convex, increasing.

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