Time-to-first-solve (TTFS)

[frapac]

Now that the StridedOneVector PR #174 has been merged, we can focus on the time to first solve.

Using the following script:

using MadNLP
using MadNLPTests

nlp = MadNLPTests.HS15Model()
ips = MadNLP.InteriorPointSolver(nlp)
@time MadNLP.optimize!(ips)

MadNLP takes for the first solve:

Total wall-clock secs in solver (w/o fun. eval./lin. alg.)  =  8.082
Total wall-clock secs in linear solver                      =  0.590
Total wall-clock secs in NLP function evaluations           =  0.037
Total wall-clock secs                                       =  8.709

EXIT: Optimal Solution Found.
  8.147811 seconds (24.28 M allocations: 1.187 GiB, 6.16% gc time, 99.93% compilation time)

It would be ideal if we can decrease that time to improve the user experience.

[sshin23]

would be interesting to add benchmark code

[sshin23]

@frapac Now that we support v1.9, might be good to revisit this and create a precompilation function