When your optimizer silently returns the wrong answer (and how to catch it) (opens in new tab)

Numerical solvers have a failure mode that is worse than crashing: every so often they return status: Optimal and hand you a number that is simply wrong. No exception, no warning — just a confident, incorrect optimum. If that number drives a downstream decision (a schedule, an allocation, a price), you may never notice. I ran into a clean example of this in HiGHS recently while reducing a bug that had surfaced through cvxpy, and the debugging path generalizes to any LP/QP/MILP stack. Here's t...