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Clarify scipy linprog transformation description #742

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Clarify scipy linprog transformation description
Zhengyizhe0209-arch May 18, 2026
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Revise linprog description after review
Zhengyizhe0209-arch May 25, 2026
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6 changes: 3 additions & 3 deletions lectures/lp_intro.md
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Expand Up @@ -487,11 +487,11 @@ The optimal plan tells the factory to produce $2.5$ units of Product 1 and $5$

We are using the `linprog` function as a *black box*.

Inside it, Python first transforms the problem into standard form.
SciPy accepts inequality constraints in the form $A_{ub} x \leq b_{ub}$, equality constraints in the form $A_{eq} x = b_{eq}$, and variable bounds.

To do that, for each inequality constraint it generates one slack variable.
In this lecture, `linprog` uses SciPy's default `highs` method, which calls the HiGHS optimization solver.

Here the vector of slack variables is a two-dimensional NumPy array that equals $b_{ub} - A_{ub}x$.
The slack value returned by `linprog` is a one-dimensional NumPy array whose entries measure the difference $b_{ub} - A_{ub}x$ for each inequality constraint.

See the [official documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linprog.html#scipy.optimize.linprog) for more details.

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