Not reaching optimal solution

[cjg...@umich.edu]

I have a relatively small optimization problem (I think) which is not
coming to the optimal solution. I know it is not reaching the optimal
solution because I am testing it with a data set from which the optimal
solution was computed and I know the optimal solution. I am doing this
to see if this optimization is working which will then be applied to
other situations.

The problem is convex and I tried solving it in Matlab, however the
gradient of the solution was not zero, thus the optimal solution was
not reached. This is one reason why I am trying AMPL.

I have been using MINOS and CPLEX as solvers, and neither have yielded
the optimal solution. Another thing which is odd...the solutions from
MINOS and CPLEX do not match. Does this say that I am assuming
something about my problem which is not true?

Any other thoughts? Thanks a lot.

Chris

[Robert Fourer]

Chris,

CPLEX only handles linear and convex quadratic problems, so if you are able
to use CPLEX then you must have a convex problem. I would check first to be
sure the CPLEX and MINOS gave an "OPTIMAL SOLUTION" message; in some cases
they will tell you that a solution is suboptimal but will return it anyway.

Also you should check that CPLEX and MINOS are supplying a worse objective
value than the one you know of. If they are finding different solutions
(values for the variables) with the same objective value, then there is
nothing wrong in your situation.

Otherwise, I would suggest taking your known optimal solution and assigning
it to AMPL's variables. (You can do this with data statements, as for
parameters, or with "let" statements.) Then use "display" statements to
check that your solution has the optimal value that you expect, and that all
of the constraints are actually satisfied. This could turn up an error in
your solution or in your model.

If you're still stuck, you might try posting your model and data for others
to look at.

Bob Fourer
4...@ampl.com