How can I fit a polynomial to an empirical data set using python such that it fits the "top" of the data -- i.e. for every value of x, the output of function is greater than the largest y at that x. But at the same time it minimizes this such that it hugs the data. An example of what I'm referring to is seen in the image below:
You need to use
cvxoptto find the coordinates of the efficient frontier, which is a quadratic programming problem, then feed those coordinates in numpy's ployfit to get the polynomial fitting the frontier. This Quantopian blog post does both: https://blog.quantopian.com/markowitz-portfolio-optimization-2/