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The method of Lagrange multipliers finds critical points (including maxima and minima) of a differentiable function subject to differentiable constraints.

5 votes

KKT in a nutshell graphically

f(x) being convex is necessary for KKT to be sufficient for x to be local minimum. If f(x) or -g(x) are not convex, x satisfying KKT could be either local minimum, saddlepoint, or local maximum. g(x) …
Mark L. Stone's user avatar
7 votes
Accepted

Lagrangian multiplier: role of the constraint sign

There is no sign restriction for the Lagrange multiplier of an equality constraint. Lagrange multipliers of inequality constraints do have a sign restriction. You should really look at the Karush- …
Mark L. Stone's user avatar