# Maximizing $l_1$-normalized entropy using CVXPY

Suppose that $$x = (x_1, ..., x_n)$$ is a vector of variables and I would like to maximize the Shannon entropy of $$\frac{|x|}{||x||_1}$$ (i.e. the vector of absolute values of $$x_i$$, normalized to have $$l_1$$ norm = 1) subject to some linear constraints. However, this function is not directly expressible as a composition of atoms recognized by CVXPY as convex/concave (although CVXPY recognizes entropy itself). Are there any tricks to write this program in a way suitable for CVXPY?

• What is the "abs value of $x$", $|x|$? Do you mean the $l_2$ norm? Jul 12 at 13:19
• Edited to clarify. Jul 12 at 20:08
• Then can you define what the Shannon entropy of a vector is? Jul 12 at 21:58
• Are you able to prove the function is convex? Jul 13 at 16:14
• Maybe use a general purpose NLP solver instead. Jul 13 at 20:53