```markdown
### Geometric Programming

#### Monomial Function

\[ f(x) = c x_1^{a_1} x_2^{a_2} \cdots x_n^{a_n}, \quad \text{dom } f = \mathbb{R}_{++}^n \]

- \( c > 0 \)
- Exponent \( a_i \) can be any real number

#### Posynomial Function

Sum of monomials:

\[ f(x) = \sum_{k=1}^{K} c_k x_1^{a_{1k}} x_2^{a_{2k}} \cdots x_n^{a_{nk}}, \quad \text{dom } f = \mathbb{R}_{++}^n \]

#### Geometric Program (GP)

Minimize \( f_0(x) \)

Subject to:

\[ 
f_i(x) \leq 1, \quad i = 1, \ldots, m 
\]

\[ 
h_i(x) = 1, \quad i = 1, \ldots, p 
\]

- \( f_i \) is posynomial
- \( h_i \) is monomial

---

*A. d'Aspremont. Convex Optimization M2.*
```
