If you got everything installed, this should run:
# numpy is crucial for vectors, matrices, etc.
import numpy as np
# Lots of cool plotting tools with matplotlib
import matplotlib.pyplot as plt
# For later: scipy has a ton of stats tools
import scipy as sp
# For later: sklearn has many standard ML algs
import sklearn
# Here we go!
print("Hello World!")
Assume $f$ is some function, and $C \subset \mathbb{R}^n$ is some set. The following is an optimization problem: $$ \begin{array}{ll} \mbox{minimize} & f(x) \\ \mbox{subject to} & x \in C \end{array} $$
Its Lagrangian is $$L(x,\boldsymbol{\lambda}, \boldsymbol{\nu}) := f(x) + \sum_{i=1}^m \lambda_i g_i(x) + \sum_{j=1}^n \nu_j h_j(x)$$ of which $\boldsymbol{\lambda} \in \mathbb{R}^m$, $\boldsymbol{\nu} \in \mathbb{R}^n$ are dual variables
The minization is usually done by finding the stable point of $L(x,\boldsymbol{\lambda}, \boldsymbol{\nu})$ with respect to $x$
Instead of solving primal problem with respect to $x$, we now need to solve dual problem with respect to $\mathbf{\lambda}$ and $\mathbf{\nu}$