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LFortran sounds to be a genenius project. The interactivity is a critical block that is missing from FORTRAN ecosystem. Hope things will get better with LFortran!
According to the papers metnioned by others, the algos under discussion do not seem to support this point. The author of the project mentiones that the FORTRAN 77 implementation is `nontrivial to understand', which motivates this work.
`Caveat: derivative free optimizers are terrible for constrained optimization however (especially if your constraints are anything but simple bounds). You can use barrier methods but still they’re not great.'
Lincoa and cobyla in the package can handle problems with nontrivial constriants according to the documentation of the git repository, though I do not know how well they work.