Lagrangian Function and Lagrangian Duality
IMPORTANT: This note is translated by LLM and fixed manually. See Chinese version for a more accurate note 1. Method of Lagrange Multipliers 1.1 Basic Definition Lagrange first proposed the Method of Lagrange Multipliers for equality constraints. Consider the following optimization problem: $$ \begin{aligned} & \text{minimize} \quad & f_0(x)& \\\\ & \text{subject to} \quad & h_i(x) & = 0, \quad i=1, \cdots, m \end{aligned} $$Then we have the Lagrangian function: ...