Monday, September 29, 2008

GBD feasibility cut

>Dear Mr. Kalvelagen,
>
>I am trying to do a comparison between the performance
>of GBD and OA in the case of convex and nonconvex minlp
>problems.
>
>I am using the GBD-code from the script for MINLP methods
>that you have written and posted on your page, and comparing
>it with DICOPT-OA. My application is on transportation
>network design problem. The theory as highlighted in Floudas
>1995 about the difference between the two methods seems to
>match for the most part in my problem. However, I am facing
>infeasibilities in the sub-problem.
>
>Your GBD code on the portfolio optimization generates support
>functions only from the feasible primal. Can you give me an
>idea (if that is not much of a hassle for you) how a
>feasibility primal subproblem can be implemented in your
>GBD code to generate additional supports (from the infeasible
>subproblems), or if you have provided an example of such a
>case somewhere else I’d be grateful if you can direct me to that?
>
>I do find your webpage and the relevant files very useful when
>testing theoretical concepts through implementation in GAMS.
>
>Many thanks in advance for your time!


You can add feasibility cuts by forming a feasibility subproblem.

I do something like that for the dual subproblem in http://amsterdamoptimization.com/pdf/benders.pdf

A straightforward discussion can be found in Ullmann's Modeling and Simulation By Fritz Ullmann page 113, and 116.

Of course it may be possibly to bypass the problem by formulating an elastic version such that the subproblems are always feasible.