Adding a quadratic constraint as a ratio of two expressions to a model
AnsweredI am writing an optimization problem using GurobiPy. My constraints are in the form of rational expressions. For e.g., assume the Model has one decision variable, 'c', and a bunch of penalty variables, where I want to minimize the sum of the penalty variables. A minimal working code is:
import gurobipy as gp
from gurobipy import GRB
n_pen = 6
m = gp.Model()
var = []
var.append(m.addVar(lb=c_lb, ub=c_ub, vtype=GRB.CONTINUOUS, name=("c")))
for i in range(n_pen):
var.append(m.addVar(lb=pen_lb, ub = pen_ub, vtype=GRB.CONTINUOUS, name=("n_pen%d" %i)))
m.update()
m.setObjective(gp.quicksum(var[i] for i in range(1,n_pen+1)),GRB.MINIMIZE)
The constraint is of the form:
c^4/(2*(c^4-1))+n_pen0 == 1
I know raising a variable to a power of '4' is not possible directly and neither can I have an expression in the denominator. For the denominator part, the constraint can be modified to c^4 - 2*c^4*n_pen0+2*n_pen == 2 but it gives another problem, a constraint probably cannot be built as a product of three terms.
Is there a way to write a constraint for the expressions I listed above?
regards,
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Gurobi Staff
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Hi Syed,
Did you have a look at our Knowledge Base articles How do I model multilinear terms in Gurobi? and How do I divide by a variable in Gurobi? For the polynomial terms, you might want to use the addGenConstrPow() or the addGenConstrPoly() function.
These most likely will provide you the answer.
Best regards,
Jaromił0 -
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Hi Jaromil,
Thanks for your response. I did not look at the two articles you referred to but I was able to resolve this last night by just using the addGenConstrPow() to generate my power terms and then add the expression directly as a constraint. For the division, I cross multiplied to remove any denominator term. I didn't use addGenConstrPoly() but it may help in having a clean code.
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