```markdown
### Force Field Interpretation

#### Centering Problem (for problem with no equality constraints)

- **Objective**: Minimize \( t f_0(x) - \sum_{i=1}^{m} \log(-f_i(x)) \)

#### Force Field Interpretation

- \( t f_0(x) \) is the potential of force field \( F_0(x) = -t \nabla f_0(x) \).
- \( -\log(-f_i(x)) \) is the potential of force field \( F_i(x) = (1/f_i(x)) \nabla f_i(x) \).

#### Force Balance

The forces balance at \( x^\star(t) \):

\[
F_0(x^\star(t)) + \sum_{i=1}^{m} F_i(x^\star(t)) = 0
\]

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