Duals for MIQCP

[Anjula-Antonis]

Hi,
I have a mixed-integer QCP code. I need to extract the dual solutions for this. I didn't find an option for fixed start in docplex. Can someone please help

[vberaudi]

if I don't mistake, you only have to do:

    model.solve()

    c = model.get_cplex()
    values = c.solution.get_dual_values([c1.index, c2.index, ...])
    print(values)

where c1, c2,... will be your constraints.
which will internally call the getpi function based on your input. Seehttps://www.ibm.com/docs/en/icos/22.1.0?topic=SSSA5P_22.1.0/ilog.odms.cplex.help/refpythoncplex/html/cplex._internal._subinterfaces.SolutionInterface-class.html

When docplex does not provide built-in functionalities, you can always get to the under lying cplex object and get the "low level" api which handles indexes.

[Anjula-Antonis]

Hi,
Thank you for the suggestion. But this doesnt work in my case since it is a mixed-integer problem. Also the option of fixed-MILP in cplex doesn't work for me since my problem in MIQCP

cplex.exceptions.errors.CplexSolverError: CPLEX Error 1017: Not available for mixed-integer problems.

[AndrasKiss]

Hi,
I'm facing the exact same problem and couldn't find a method to solve fixed MIQCPs anywhere (to get the dual values for some of the linear constraints, in my case). I suppose reformulating the model by hand with the optimal integer solutions as constants would work. Is that the only option though? Help would be very much appreciated.

[PhilippeCouronne]

Hello,

I have committed a small sample to show how to fix values for a MIQP, solve it as a QP and access dual values.
The idea is to change the CPLEX problem type to "fixed_MIQP" once it has been solved successfully.
As this modification can lead to tricky errors, I encapsulated it in a context manager to ensure I get back the original model
unchanged at the end.

The sample:

https://github.com/PhilippeCouronne/docplex_contribs/blob/master/docplex_contribs/src/miqp_duals1.py

Hope this helps

[AndrasKiss]

Hi Philippe,

Thanks for your work! I've already come across a similar code segment of yours from June 2021 on an IBM Community site. That one was for MILP -> fixed MILP.

The reason neither of these segments solve my problem (or the OP's problem) is that we are looking for MIQCP -> fixed MIQCP. And the reference manual says that there is no ProblemType value for fixed_MIQCP.

As for me, I've already figured out how to work around this limitation by defining a second QCP model based on the solution values of the first MIQCP. But it would still be nice to know if there is an officially supported way of running a fixed version of an MIQCP model and calculating the duals from it. Please let us know if you have other ideas, or if something is incorrect in my diagnosis above.

[PhilippeCouronne]

Hi,
My bad, I missed you had a MIQCP. You are right, there is no fixed MIQCP so my code won't work for MIQCP. I'll come back to you if I find some way to work this around,
In addition, I'm curious about how you managed to define your fixed QCP. I guess you changed variables to continuous and constrained variables in intervals with some precision values?

[AndrasKiss]

Hi Philippe,
I somehow missed your question in the second line at first reading, sorry about that! I only had binary non-continuous variables, and I simply substituted their optimal values as constants at the second QCP run.

For example:
Suppose x may be either 0 ("inactive") or between 0.5 and 1.0 ("active"). In the MIQCP, I define x as continuous between 0 and 1, and a second, binary variable z, which is either 0 or 1. Then I add the following constraints:
0.5 * z <= x
x <= z
Essentially, z records whether x is active or inactive.

Once I solve the MIQCP, the optimal value of z tells me whether x will be active (z = 1) or inactive (z = 0) at the optimal solution. So I redefine a QCP with x only, and substitute either z = 1 or z = 0 into the two constraints above. Either way, optimizing the QCP will give me the same optimal x as the MIQCP did, but now I can query the duals on (some other) constraints that I'm interested in.

This may be too specific to my application to be useful to others, though. I haven't thought much about generalizations.

[PhilippeCouronne]

Thanks Andras, this is fairly natural. I was thinking about a generalized way of doing this. Advanced features such as piecewise funtional constraints, SOS sets , indicators, equivalences should also be translated into the fixed problem. I guess you had none of them in your model. I have ideas about how to handle them; I may post a fix_model() transformation when I have time.
Thanks again for your response.