Convex Programming
AnsweredI have a convex programme with around 10 variables. Does the Gurobi Optimizer gurantee the exact solution for the convex programme?
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Gurobi Staff
Yes, as long as Gurobi is able to recognize your model as convex, it can solve it to global optimality.
What kind of model do you have in mind?0 -
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Thanks for your response.
In my model, the objective function is a sum of a few Euclidian norms and constraints are some linear inequalities. How does Gurobi work for this kind of a situation?
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Gurobi should be able to recognize the objective to be a convex quadratic term. It would then use the QP Simplex method or the quadratic Barrier method to solve the model.
In order to construct your model, you can use the addGenConstrNorm method to add your Euclidean norm terms. Since the addGenConstrNorm method creates an equality constraint with an optimization variable as result, you would have to introduce an auxiliary variable for each Euclidean Norm. So your model would look something like this
aux1 = model.addVar(obj=1, name="aux1") model.addGenConstrNorm(aux1, [list of variables in the Euclidean norm], 2.0, name="norm_1") aux2 = model.addVar(obj=1, name="aux2") model.addGenConstrNorm(aux2, [list of variables in the Euclidean norm], 2.0, name="norm_2") ...The above code snippet creates a model of the form
\[\begin{align*}
\min \,\,\,&\text{aux}_1 + \text{aux}_2 + \dots\\
\text{s.t.} \,\,\, &\text{aux}_1 = \sqrt{\sum \text{vars}^2} \\
&\text{aux}_2 = \sqrt{\sum \text{vars}^2}
\end{align*}\]Best regards,
Jaromił0 -
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Thank you very much Jaromił; it was really helpful
I will proceed accordingly. If we get any quires, we will reply on this comment chain.
Kind regards,
Oshan
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