Model with bilinear and 'sigmonial' constraints can not be solved

[LYC]

Hi, Johan,

I have a model such as :

 

where S(njat) is a function of variable (njat), when i build this model using Yalmip. some of the constraints description are as follows:

#212|    Equality constraint (bilinear) 1x1|       1.0851e-07 to 1|

#317|   Equality constraint (sigmonial) 1x1|       1.2057e-08 to 1|

I am not sure what type of this model, so I have tried some solvers such as fmincon. Gurobi, bmibnb, sedumi, all of them cannot give a solution. So I wonder if the model is built incorrect or the solvers are not appropriate.

The code is attached.

Thank you.

[Johan Löfberg]

You have a nasty mixed-integer nonlinear model. You are very optimistic to believe you can solve this model.

You cannot use gurobi since the model isn't a bilinear model (you have  S(t-1) / ( S(t-1) + E(t-1) + R(t-1)  which are the terms which lead to the term signomial). I guess you could get it bilinear by multipling the equalities where Pcts occur by the denominator and thus setup a bilinear equality instead S(t)* (S(t-1) + E(t-1) + R(t-1) ) == ...

However, I would estimate the likelihood of this model being solvable globally as roughly 1/inf