Betts 10 47

[Peter230655]

This may be a candidate for examples-gallery for these reasons:

• It is a three stage problem, where the results of the previous stage are the initial conditions for the next one. There is no example like this in examples-gallery, to my knowledge.
• The second stage is a singular arc (see section 4.16.1 for some explanation). I do not think, opty allows to incorporate the additional boundary condition needed, so I just ignorted it. As per John Betts ignoring it may make the result less reliable.
• In the first stage opty does not converge, no matter what I tried. Yet the results are good. So, maybe one should not immediately discard a result of opty simply because opty says it did not converge. Update 1-5-25: Now that I include this boundary condition, also the first stage converges rapidly
• The results given in the book differ from the results John Betts sent to me by email, by 0.5..0.6 %. So, it seems to me the difference between opty and Betts' results are acceptable.

[Peter230655]

I made some mistake with git!

[Peter230655]

Just for information: These are the result John Betts sent me by email.
cdsosn_gdrd07.out.zip
cdsosn_gdrd07_barrier.zip

[Peter230655]

When I pushed this initially, I did not know how to handle nontrivial instance constraints, depending on state variables and control variables, so I ignored it.
Now that I know how to do it, I included it.

Really all this shows is how to handle a multi-staged optimization, where the results of the i-th stage are the initial values of the (i+1)-th stage - no stroke of genious. I guess, ideally all stages should be optimized simultaneously, but I would not know how to do this. I do not know, whether Betts does it sequentially or simultaneously in any case my sequential results are close to his.