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### (Generalized) Linear-Fractional Program

#### Objective
Minimize \( f_0(x) \) subject to:
- \( Gx \preceq h \)
- \( Ax = b \)

#### Linear-Fractional Program
\[ 
f_0(x) = \frac{c^T x + d}{e^T x + f}, \quad \text{dom } f_0(x) = \{ x \mid e^T x + f > 0 \} 
\]

- A quasiconvex optimization problem; can be solved by bisection.
- Also equivalent to the LP (variables \( y, z \)):

#### Equivalent Linear Program
Minimize \( c^T y + dz \) subject to:
- \( Gy \preceq hz \)
- \( Ay = bz \)
- \( e^T y + fz = 1 \)
- \( z \geq 0 \)

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_A. d’Aspremont. Convex Optimization M2._ (Slide 52/67)
```