Originally posted by: Bogdan_Tanasa

I have a problem which has quadratic constraints of the form:
sum x_i * y_i <= K

I would like to keep each product x_i * y_i in a different array and to re-write the initial constraint in the form sum z_i <= K where z_i = x_i * y_i;

If I define z_i = x_i * y_i then CPLEX says the Q matrix is not semi-positive definite.
Is there any way to have this products stored in a array without getting the convexity error ?

Thanks,
Bogdan.
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Originally posted by: SystemAdmin

And you do not get the error message if you write sum x_i * y_i <= K?
What API do you use? If you use concert then you could just keep the products x_i * y_i in an array of IloExpr or IloLinearExpr without adding the new z variables. An IloExpr can be used almost everywhere an IloNumVar can be used, so using the products would still be simple.
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Originally posted by: Bogdan_Tanasa

dvar int xhttp://1 .. 5 in 0 .. 1;
dvar int yhttp://1 .. 5 in 0 .. 1;

subject to {
sum(i in 1 .. 5)x[i] * y[i] <= 10;
}

does not say anything related to convexity.

Do you think it should ?
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