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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: grad f = sum_i a_i grad c_i I imagine that the algorithm knows about them, but I can't find the relevant method to extract it.

When using Mixed Integer Linear Programming to find the minimum of a linear function f(x_1,...,x_n) $f(x_1,...,x_n)$ under a set of constraints c_i(x_1,...,x_n) $c_i(x_1,...,x_n)$ (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: grad $$\text{grad} f = sum_i \sum_i a_i grad c_i \cdot \text{grad} c_i$$ I imagine that the algorithm knows about them, but I can't find the relevant method to extract it.

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 $a_i$ 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.