Lagrange multipliers

(1.3 hours to learn)


Lagrange multipliers are a tool for solving optimization problems with equality or inequality constraints. In particular, some linear combination of the gradients of the constraints must match the gradient of the function. Lagrange multipliers are a key idea behind Lagrange duality, a central concept in convex optimization.


This concept has the prerequisites:

Core resources (read/watch one of the following)


Supplemental resources (the following are optional, but you may find them useful)


MIT Open Courseware: Multivariable Caclulus (2010)
Video lectures for MIT's introductory multivariable calculus class.
Author: Denis Auroux
Lagrange multipliers without permanent scarring
  • Section 1, "Introduction," page 1
  • Section 2, "Trial by example," pages 2-6
Author: Dan Klein

See also