↗

Lagrange Multipliers

Undergraduate

Definition

Lagrange multipliers method solves optimization problems with equality constraints by combining constraints with new variables (multipliers).

𝒧(x, λ) = f(x) - λ g(x)

Lagrangian

∇ f = λ ∇ g

Condition at optimum

Example 1

Maximize xy subject to x + y = 10.

Discovered by: Joseph-Louis Lagrange (1788)

Lagrange developed this method while solving mechanics problems.

Utility maximization under budget

Mechanical constraints

SVM optimization