Lagrange multiplier condition
finds the stationary point of the objective function on the equality constrained surface.
symbols, variables and units
f: target; g: constraint; λ: multiplier, whose unit is consistent with f/g.
applicable conditions and boundaries
is differentiable and constrained to be regular; it is a necessary condition and cannot determine the minimum value alone.
formula source code
The following is a copyable LaTeX expression.
\nabla f(x)+\lambda\nabla g(x)=0,\quad g(x)=0
Reference and Extended Learning
Stanford · Convex Optimization, Boyd & Vandenberghe ↗is organized according to model definition and assumptions. Please check actual conditions and original literature before engineering, research and clinical use.
Lagrange multiplierconstrained optimization