The question came up whether Cplex is the only solver that supports indicator constraints. It looks like SCIP supports these also: http://scip.zib.de/doc/html/cons__indicator_8c.html. I tried this with the the NEOS setup at http://www-neos.mcs.anl.gov/neos/solvers/milp:scip/AMPL.html but that seems to have a rather unsophisticated AMPL link to put it mildly. As only minimization is allowed it looks like it is going through an MPS file. As a result the AMPL indicator constraints are also not available. The error message I receive when I submit a test model with an implication is a little bit off:
ERROR: Runtime error encountered
2 variables, all nonlinear
0 algebraic constraints
1 logical constraint
1 linear objective; 2 nonzeros.
Problem has 2 nonlinear variables. No MPS file written.
Please correct and resubmit.
The model is really linear. I suspect AMPL uses nonlinear functions as a mechanism to communicate the logical constraints with the solver.
I like the concept of indicator constraints and how they are implemented in AMPL (http://www.ampl.com/INFORMS06.pdf). I would certainly hope other solvers would also move into this direction. Given the increasing attention for Constraint Programming, it makes sense to expect that these features get more traction. I also tried to check the GAMS documentation on GAMS/SCIP to see what GAMS has to offer here. Unfortunately the documentation for GAMS/SCIP is largely nonexistent: http://www.gams.com/dd/docs/solvers/coin.pdf.
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