Writing belongs to constraint with gurobipy
OngoingI am trying to add this constraint to my model.
I have added all the constraints except the last one. How to write this constraint when a variable belongs to a set. Thanks

Could you post a minimal working example of what you are currently trying to implement?
How to write this constraint when a variable belongs to a set.
Depending on how you define your variable in your code, you can define a list of indices and loop over those, e.g.,
import gurobipy as gp
m=gp.Model()
x = m.addVars(10)
U = [0,1,2,3]
m.addConstrs((x[u] <= 2) for u in U)constructs the constraints \( x_u \leq 2 \quad u \in U = \{0,1,2,3\}\).
Best regards,
Jaromił0 
Hi Jaromil,
Thanks for the reply. Here is the problem I am trying to solve:
U_1 = {1,2,3,..L}
U_2 = {1,2,3,..K}
R=
r^{u}_{t,f} is the cost function. I have to maximize the above objective function using constraints C1,C2, and C3 in the above problem I have posted before. Here is the code I wrote:
T = (np.arange(1,21,1))
#print(len(T))
F = (np.arange(1,101,1))
M = np.arange(1,11,1)
E = (np.arange(1,6,1))
U = (np.arange(1,6,1))
assignment_model = grb.Model('Assignment')x = assignment_model.addVars(M.shape[0], T.shape[0], F.shape[0], vtype = grb.GRB.CONTINUOUS, lb = 0, ub = 1,name = 'x')
assignment_model.addConstrs((sum(x[u, t, f] for u in range(E.shape[0]) for u in range(U.shape[0])) <= 1 for t in range(T.shape[0]) for f in range(F.shape[0])), name = 'one RB allocation')
assignment_model.addConstrs((sum(x[u,t,f] for t in range(T.shape[0]) for f in range(F.shape[0])) >= 1 for u in range(U.shape[0]) ), name = 'latency requirement')
obj_fun = sum(se_e_power[p][u,t,f] * x[u,t,f] for u in range(E.shape[0]) for t in range(T.shape[0]) for f in range(F.shape[0])) + sum(se_u_power[p][u,t,f] * x[u,t,f] for u in range(U.shape[0]) for t in range(T.shape[0]) for f in range(F.shape[0]))
assignment_model.setObjective(obj_fun, grb.GRB.MAXIMIZE)
assignment_model.setParam('OutputFlag', False)
assignment_model.optimize()
#print('Optimization is done. Objective function value: %.2f' % assignment_model.objVal)
value = assignment_model.objValIt looks like I wrote the third constraint as you suggested. But the output is not as expected. Please let me know if there is anything wrong with code.
Thanks
0 
Hi Venkateswarlu,
The constraint
assignment_model.addConstrs((sum(x[u,t,f] for t in range(T.shape[0]) for f in range(F.shape[0])) >= 1 for u in range(U.shape[0]) ), name = 'latency requirement')
Looks OK. Did you write the model to an LP file and inspect it to see whether all constraints look as expected?
assignment_model.write("myLP.lp")
The write method will write a humanreadable LP file which you can inspect.
Best regards,
Jaromił0 
Hi Jaromil,
I am using the write command, but I do not see any output. I updated the version to latests but I do not see any output.
Any suggestions?
Thanks,
Venkat
0 
Hi Venkat,
The write method will generate a file in the folder from which you execute your script. It will not print anything to the console output or the log.
Best regards,
Jaromił1 
I can see the output now
0 
Hi,
I guess I solved the issue after printing it. Thanks for the suggestions.
One more question is what kind of algorthim the libraray is using. As my problem is convex optimization, I was looking into theorteical concept of solving the problem. It was explained there are many algorthims to solve it. What exactly the algorthim it uses when I write grb. Maximize(like subgradient or Newtons or lagrangian). Is there any documentation which explains the algaorthim the library is using?
Thanks,
Venkat
0 
Hi Venkat,
You can find some basics on convex continuous programming at Linear Programming (LP)  A Primer on the Basics. There at the bottom, you will find the literature for the algorithms you seek.
Best regards,
Jaromił0 
Hi Jaromil,
Thanks for the information.
I have a quick one. I am trying to write the following constraint but I am getting an error. Could you suggest me how to write the following expression? t,f are for all. R_min is a constant.
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