The problem which we are going to study is an convex problem with affine equality constrains.
where A belongs to R+^{pxn}, rank(A) = p and b belongs to R+{p}.
An extremely good approach of the problem's solution can be obtained via CVX which is a Mathworks product. Further information in the link below
After that we perform again the search of a feasible point x0 with CVX having under consideration that
x0 > 0 & Ax0 = b
Then we use the above x0 to implement the Newton algorithm for finding a feasible point x0. Newton's method was implemented with backtracking.
Now, we notice that not only the output from the CVX solution method but also the output from Newton's method converge to a feasible point x0. Of course, there are some deviation but we can ignore it.
Now, its time to solve the dual problem of the problem above again using the CVX. We notice that the solution of the dual problem is identical with the solution of the primal problem, a result that was expected.
