Embedded PERK 2-3

[warisa-r]

Here to keep track of all my embedded PERK scheme attempt

• Base with changed function of a_unknown and polynomial optimizer to something that can also take num_stage_evals. + matrix that solve b
• Solve a_unknown using JuMP and Ipopt is based on Base using_JuMPIpopt_a_unknown
• Find c using JuMP and Ipopt so that a_unknown and b_embedded are positive. -> Merge two functions into one could solve the existing error using_JuMPIpopt_c.
  Result: Converged to a point of local infeasibility. Problem may be infeasible.
• Optimize the polynomial and use a, b, and c as free parameters using Ipopt: using_JuMPIpopt_mon_coeffs. -> not functioning right now

All branches are outdated with the main trixi.