Can this be implemen

[Frans Janss]

Hi,

As an practical assignment I am supposed to implement something like this optimization problem:

http://www.biomedcentral.com/1471-2105/9/43/figure/F2  (part B)

First of all, I want to make sure if this is a typical problem that can be solved via YALMIP.  Without going into detail, the objective is to reduce the difference between a computed vector and some know constants (experimental).  How can I set an objective with a summation in YALMIP for example? I don’t expect from you to solve all my problems at once, but the main question is if this is a common problem for YALMIP with this kind of objective and constraints.

(I do have a matlab and gurobi license)

Frans

[Johan Löfberg]

Yes, it looks like a standard gene knockout problem, which is a bilevel program. Bilevel programs are extremely hard to solve, and although this specific problem has some beneficial features, it is still pretty hard to solve, so I would prefer to do it using specialized software (optknock) which takes problem-specific shortcuts.

I played around with these models some months ago, and they are utterly sensitive to modelling choices, when trying to solve them using a generic bilevel programming framework (such as YALMIP). Alternatively, derive the MILPs, which the bilevel program gives rise to, and implement that using YALMIP. That way some of the problem specific stuff is exploited (the kkt conditions simplify significantly in these models compared to generic bilevel programs)

[Johan Löfberg]

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Solvebilevel
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.BilevelProgramming
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Kkt

[Frans Janss]

Thanks for your advice. I think I can get the MILP formulation of this problem. Then I will try to use YALMIP to solve it. Thank You.

Frans

[Johan Löfberg]

If you try to implement the gene knockout bilevel program, it is of fundamental importance that you exploit the fact that the complementary slackness conditions simplify and turn convex in this particular example. The generic problem description leads to a basically useless model.

http://maranas.che.psu.edu/pub/burgard-etal03a.pdf