Lagrange function


## **Lagrangian**
$$L(x, λ) = f(x) + λg(x)$$
f(x) is [Objective function](https://texonom.com/objective-function-5bf6c1fc7c854b5aaaacd17d5e094464) , g(x)는 [Optimization Constraint](https://texonom.com/optimization-constraint-1e59b72826004f059cd7e1b00f8a9721). 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 [Lagrange function](https://texonom.com/lagrange-function-922d5624e8bf46c8b86537720c5a053c) for each [Optimization Constraint](https://texonom.com/optimization-constraint-1e59b72826004f059cd7e1b00f8a9721) 
We might derivate Lagrange function and find w which minimize
Check this is not max and min. not argmax
### Lagrange function Notion
|Title|
|:-:|
|[Lagrange multiplier](https://texonom.com/lagrange-multiplier-1e414a17f1074b9eb4e5668ceacb46d6)|
|[Lagrange Duality](https://texonom.com/lagrange-duality-8de2c3f1399e4765ba2543d4e8360eeb)|
|[Karush-Kuhn-Tucker Condition](https://texonom.com/karush-kuhn-tucker-condition-01c654c038e1493080cbcb9ec1d026d0)|









