Symbolic Optimization

Specific Domains Optimization (Mathematical)
1

Hello,

Is there a way to use Julia to solve for symbolic optimization problems. What I have in mind is something that works like Mathematica (or Wolfram Alpha) but with a nice syntax and decent computation speeds that can give me the value of an optimizer by cases (as a function of parameters). The problem is very simple:

using Symbolics, ModelingToolkit

@variables νa νb μ
@parameters Ca Cb σ χ z τ

problem = νa*Ca + νb*Cb + χ*μ^(1-σ)

@named sys = OptimizationSystem(problem,[νa,νb,μ],[Ca,Cb,σ,χ,z,τ])

u0 = [
    νa=>0.0
    νb=>0.0
    τ*(1/z+νa)=>μ
    τ*(1+νb)=>μ
]