cutting-plane method with equality constraint

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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: $$ - x_1 + \frac{x_2}{x_3} \leq 0\\ x_1 - \frac{x_2}{x_3} \leq 0 $$