如何在Gurobi中编码线性组合

Question

I have found the following example as on how to code the constraint "the sum over all a_{i,j}*x_{i,j} with j element of J is <=5 for all i in I". (sorry, I don't know how to properly write this in code, here is a first try):

\sum{a_{i,j}*x_{i,j}} <= 5 

in Gurobi python:

m.addConstr(x.prod(a,i,'*') <=5 for i in I)

I would really appreciate if someone could explain this expression to me!

Here is what I understand: m is usually used as a variable to store the model, in a program we would start with m = Model() to create an empty model. We add one constraint with addConstr() and x must have been introduced as a variable. the x.prod() method creates a linear combination of its parameters. However, I don't know how to interpret the three parameters a, i, '*' i is part of the for loop, it starts with 1 and then gets incremented by one until the last element of I is reached. '*' is used as a wildcard and will address just any element. But what does this combination of a, i, '*' tell me?

Answer 1

a is a parameter and has two index i,j. ' * ' means for all j. Using ' * ', you don't need "for loop" for j like, "for loop" for i. You can see that in explicit form at the slayt which has two "for loop".