CasADi allows to discretise a minimum-time OCP using the collocation method and construct an equivalent nonlinear programming with the final time as an augmented decision variable 。
Is ampl OK?
CasADi is a modeling system separate from AMPL, so I have only limited information about it.
After CasADi constructs an equivalent nonlinear programming problem (with the final time as a decision variable), it might be able to write the problem in AMPL’s “.nl” format, which can be sent to any AMPL-enabled solver. Have you seen any CasADi documentation for doing that? And if so, can you provide a link to it? Maybe then I can say more about the connection to AMPL that is being used.
More generally, if you are looking at any documentation for CasADi that mentions a connection to AMPL, you may want to post a link to it here, to get some help. Also you can try the CasADi help forum at casadi/casadi · Discussions · GitHub.