Function applied to variable for more flexible domain
AnsweredOptimizing a problem f(x), where 0.0 <= x <=1 .0
Is it possible to achieve below when solving x?
when x < threshold, x== 0
when x >= threshold, x== x
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Gurobi Staff
You can define x as a semi-continuous variable. A semi-continuous variable has the property that it takes a value of 0 or a value between the specified lower and upper bounds. With the Python API, you can define your x variable as follows:
x = model.addVar( lb = threshold, vtype = "S", name ="x")
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Thank you. I'll try it out
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Have checked that it would work as expected. Would it be possible to mix it with the continuous variable? For example, set x1-x5 to be semi-continuous and the rest to be just continuous
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Yes, a model can have both semi-continuous and continuous variables.
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Sorry I meant mixing semi-continuous and continuous for a variable with length n
That sounds like just using different ub/lb for each x_i. Could you confirm?
For example,
n = 10
threshold = 0.2
lb = np.zeros(n)
lb[0] = threshold
x = model.addVar(n, lb=lb , ub=1.0, vtype="S", name="x")But if want to pin my x_i (ub and lb are the same), can it still by any chance bring it to 0?
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One approach to do this would be to set the "vtype" attribute for the variables according to the types you want. In the example below, x[0], x[1], and x[2] will be semi-continuous variables with lower bounds of 1, and x[3] and x[4] will be continuous variables with the default lower bound of zero.
lb = [1,1,2,0,0]
x = m.addVars(5, lb=lb, vtype=["S" for _ in range(3)] + ["C" for _ in range(2)], name="x")I hope this helps.
Best regards,
Simran0 -
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That's what I'm looking for. Thank you!
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