Lesson 42 of 48
Lagrange multipliers
Optimising when you are not free to go anywhere.
Most real optimisation is constrained: a budget, a norm, a probability that must sum to one. The multiplier trick turns “subject to” into an ordinary stationary-point problem.
Do this
Maximise a function subject to a constraint using Lagrange multipliers, by hand. Verify by sampling many points along the constraint curve and confirming none beats your answer.
The question that unlocks the next lesson
At a constrained optimum, how do the two gradients relate?
- AThey are perpendicular
- BThe objective's gradient is parallel to the constraint's gradient
- CBoth are zero
- DThe constraint's gradient is zero