Lagrange Function

L(x, λ) = f(x) + λg(x)

f(x) is

Optimization Constraint. λ는 Lagrange multiplier and general version is

L(w, \alpha,\beta) = f(w) + \Sigma_{i=1}^k \alpha_ig_i(w) + \Sigma_{i=1}^k\beta_ih_i(w)

and then take derivative to this function by

w

We need

We might derivate Lagrange function and find w which minimize

Check this is not max and min. not argmax

Lagrange function Notion