I'm trying to use a cutting plane algorithm to minimize a convex objective and constraint.
The constraint is an equality constraint, however, and the algorithm only specifies how to work with inequality constraints.
Imagine the constraint to be :
$$ - x_1 + \frac{x_2}{x_3} = 0 $$
Is it valid if I change this to two constraints: $$ - x_1 + \frac{x_2}{x_3} \leq 0\\ x_1 - \frac{x_2}{x_3} \leq 0 $$