JuMP.jl to solve NLP with higher exponents?

Wondering what is the best solver for Non Linear programming for the objective function with exponent 4 and 5? I am trying to solve for a big graph of the order 20k vertices and 1M edges.

Please advise any documentation.

Welcome! I’ve moved your post to the “Optimization (Mathematical)” section, which is where we try to keep all of the JuMP-related questions.

Without knowing more about your problem, the first nonlinear solver to try, always, is Ipopt: GitHub - jump-dev/Ipopt.jl: Julia interface to the Ipopt nonlinear solver

But Ipopt doesn’t support discrete variables like binary or integer. And it may struggle if you have 10^6 or 10^7 variables and constraints and the problem is non-convex.

If you need more help, please post a reproducible example of your problem.