Lagrange multipliers

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When using Mixed Integer Linear Programming to find the minimum of a linear function $f(x_1,...,x_n)$ under a set of constraints $c_i(x_1,...,x_n)$ (equality or inequality constraints), I would like to have not only the solution and value but also the Lagrange multipliers for the constraints, namely values $a_i$ such that, at the critical point: $$\text{grad} f = \sum_i a_i \cdot \text{grad} c_i$$ I imagine that the algorithm knows about them, but I can't find the relevant method to extract it.