Here is a constrained entropy maximization problem:
\begin{array}{ll} \mbox{maximize} & -\sum_{i=1}^n x_i \log x_i \\ \mbox{subject to} & \mathbf{1}' x = 1 \\ & Ax \leq b \end{array}where $x \in \mathbf{R}^n$ is our optimization variable and $A \in \mathbf{R}^{m \times n}, b \in \mathbf{R}^{m}$.
To solve this, we can simply use the entropy
operation Convex.jl provides.
using Convex, SCS
n = 25;
m = 15;
A = randn(m, n);
b = rand(m, 1);
x = Variable(n);
problem = maximize(entropy(x), sum(x) == 1, A * x <= b)
solve!(problem, SCSSolver(verbose=0))
println(problem.optval)
println(x.value)
3.2188073846026657 [0.039596694193772826 0.040060435043293534 0.04019878866073644 0.03983978331717988 0.03937174306719803 0.040288113034394835 0.04068296295587558 0.040348699741541545 0.03977943218842446 0.03920155057856007 0.03967456574632815 0.03965070447384114 0.04005546388236403 0.040085272144984585 0.04063891088176249 0.040633416079841944 0.04053676010233853 0.0401124273142282 0.04065132469849484 0.03909258717640152 0.04005131432373106 0.03929182732897887 0.04009644317279356 0.04046763019265253 0.03959301166868323]