Add a comparison with InfiniteOpt.jl (Task #5)

[frapac]

InfiniteOpt.jl is another Julia package that supports the solution of large-scale optimal control problems. It can use both JuMP and ExaModels as backend.
https://github.com/infiniteopt/InfiniteOpt.jl/

I would suggest to add a comparison between InfiniteOpt.jl and OptimalControl.jl. See e.g. the following tutorial:
https://infiniteopt.github.io/InfiniteOpt.jl/stable/examples/Optimal%20Control/hovercraft/

[ocots]

@0Yassine0 Can you try to make a comparison with this package?

[0Yassine0]

The example provided in this tutorial have constraints on intermediate values of the state.
I guess that's not allowed in OptimalControl.
I'll look for another model to use in the comparison : https://infiniteopt.github.io/InfiniteOpt.jl/stable/examples/Optimal%20Control/consumption_savings/#Consumption-Savings-Problem

[0Yassine0]

I created a small comparison between OptimalControl and InfiniteOpt in this folder.
I compared the results using plot and @benchmark from BenchmarkTools. here.
Is there any other particular comparison I should add to the notebook?

[frapac]

I just looked at the logs: Ipopt is converging in one iteration with InfiniteOpt, 4 with OptimalControl.jl. is there any reason why it is the case? Is the model a QP with only equality constraints?

I would suggest having a look at the quadrotor problem, already implemented in OptimalControlProblems.jl. You can found an implementation using InfiniteOpt.jl in that file. Do you think it's doable?

[ocots]

Clearly, the initial guess is not the same.

[0Yassine0]

By fixing the initial guess for both models, the number of iteration is now the same.

[0Yassine0]

I would suggest having a look at the quadrotor problem, already implemented in OptimalControlProblems.jl. You can found an implementation using InfiniteOpt.jl in that file. Do you think it's doable?

The quadrotor problem given in the file is not the same model we have in OptimalControlProblems.jl.
I created the similar problem in the same folder.
The comparison file is here.
Is there an explanation why even by fixing the same initial guess the first objective value given by Ipopt isn't the same for both solvers?