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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?

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

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