[hyferg]

One application of Lagrange Multipliers includes deriving the micro, standard, and grand canonical ensembles from statistical physics [0].

These can be used to simulate physical systems like magnets and particle fields.

The Lagrange Constraints are used to constrain things like probability, energy, and particle numbers. What is constrained accounts for the difference between the ensembles listed above.

The derivation of the Support Vector Machine also involves Lagrange Constraints as well!

https://en.m.wikipedia.org/wiki/Statistical_mechanics