Write python code for the barrier algorithm as outlined in the

course text.

More precisely, create a single $.$py file containing python functions for each of the following algorithms:

$$ backtracking line search

$$ KKT system builder and solver

$$ Newton$$s method for equality constrained problems using

previous two functions.

$($You can use feasible start Newton$$s method.$)$

$$ Barrier method whose centering step uses your Newton$$s

method code.

Refer to text for pseudocode for the algorithms.

Note: You may only import the libraries jax.numpy and jax for part $1.$

Using other libraries or functions which trivialize the

code$/$problem will be marked down heavily.

$($E$.$g$.,$ don$$t just import and use cvxpy$.)$