Originally posted by: EhSa

Hi,

I use CPLEX 12.4 in Matlab to solve QCQP problems of the following form:

min x'Qx
s.t.
Ax+By+Cz <= b (1)
y'y <= scaler (2)
x,y,z >= 0

CPLEX 12.4 returns the dual values associated with linear constraints in (1), it also returns a vector of reduced costs. My question is whether it is possible to extract the dual value associated with the quadratic constraint in (2) from the vector of reduced cost provided by CPLEX or not. I took a look at the Matlab example "socpex1.m" to see how one can extract the dual values associated with the qc's using the vector of reduced costs which basically requires identifying the "cone head" variable. However, here I do not know the cone head variable associated with the constraint (2), and I am not sure how CPLEX transforms this qc into the SOCP standard form.

Thanks!
Ehsan
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Originally posted by: SystemAdmin

CPLEX 12.4 only supports duals for SOC constraints. If you do not write your quadratic constraint as SOC then there is no way to get the dual values for it. This article illustrates how one can transform several types of quadratic constraints into SOCs. Maybe you can apply one of those transformations?
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Originally posted by: EhSa

Thanks Daniel for the reply!

Are you sure the link is correct?

Ehsan
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Originally posted by: SystemAdmin

Sorry, I meant to reference this article.
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Originally posted by: guabiik

Hi, i have a similar problem but i didn't find the answer in the link. 

I have a SOCP and don't know how to solve it becasue I don't know my "cone head" variables. 

 

Thanks

 

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Can't you just introspect your second order cone constraint to find the cone head variable?

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