```markdown
**Example**

Minimize:  
\[ f_0(x) = x_1^2 + x_2^2 \]  
Subject to:  
\[ f_1(x) = x_1/(1 + x_2^2) \leq 0 \]  
\[ h_1(x) = (x_1 + x_2)^2 = 0 \]

- \( f_0 \) is convex; the feasible set \(\{(x_1, x_2) \mid x_1 = -x_2 \leq 0\}\) is convex.
- Not a convex problem (according to our definition): \( f_1 \) is not convex, \( h_1 \) is not affine.
- Equivalent (but not identical) to the convex problem:

Minimize:  
\[ x_1^2 + x_2^2 \]  
Subject to:  
\[ x_1 \leq 0 \]  
\[ x_1 + x_2 = 0 \]

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