use of sos2 - PWL

[Tommaso De Marco]

Dear Professor,

I'm trying to model the non linear characteristic of of a CHP unit in an Energy Hub model. 

In particular I have to model the relation Pchp_phub(k)==Pgas_chp(k).*CHP_eff_el (valid for each timestep) in which the CHP_eff_el has to be non linear.

So, instead of writing the above constraint, in order to keep the model linear I tried to use the SOS2 to model a PWL approximation of the Pgas_chp versus Pchp_phub non linear characteristic following the SOS2 example online (https://yalmip.github.io/command/sos2/).

Gurobi tells "model is infeasible or unbounded" but I introduced boundaries for all the variables.

Do you have any suggestion on where to look for the issue and on how to solve it?

(code is attached)

Thank you very much!

[Johan Löfberg]

You can remove all constraints involving lambda, and the problem is still infeasible. Hence, you must find the reason for infeasibility elsewhere

https://yalmip.github.io/debugginginfeasible/

[Johan Löfberg]

and note tht x^1.25 is convex socp representable thus gurobi can deal with it (implemented using cpower)