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I'm trying to implement Dinur-Nissim algorithm and am stuck at how to solve the set of linear inequalities with multiple unknowns and a large number of equations along with constraints.

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Example:

\begin{align} 0.2 \leq c_4 \leq 0.66\\ 0.66 \leq c_3 \leq 1.56\\ 0.96 \leq c_3 + c4 \leq 2.26\\ \end{align}

Constraints:

$$0 \leq c_i \leq 1$$

and many other equations with the number of unknowns going up to $c_n$ where $n$ is the size of the database, so I need a solution which works for a large number of equations.

I have tried to look for some libraries but most of them solve Maximization or Minimization problems so am not sure if its possible to convert these equations to one of those problems.

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If you have a set of linear inequalities and linear equalities, you can use linear programming software to find a solution, or determine there is no solution. You can make up any (linear) objective function to be minimized or maximized, for instance, the function which equals 0.

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