Hi, thanks for this great comment!
Your first example is possible with the kind of symbolic arrays we are working on: https://github.com/JuliaSymbolics/SymbolicUtils.jl/pull/123
It does a best-effort shape propagation, but you can leave out the shape if you don’t have it.
So your example could be simply encoded by something like
@variables x::Vector
maximize(sum(1//2 .* log.(x)), st=sum(x) == I)
Where log.(x) just returns a symbolic broadcasted term.
The second one:
differentiate(1//2 .* log.(x), x)
This would require adding rules for differentiating broadcast. This is tricky but possible!
Also we could easily make
@variables n::Int x[1:n]
Work so that you can have arrays that share dimension and match them when possible…