[Coin-lpsolver] QP with CLP

[Jan-Willem Goossens]

Hi,

After years of linear programming, I'm trying my first QP..
I'm trying to solve the following problem with a quadratic objective function in CLP:

min  \sum_i ( z_i * x_i + z_i * y_i )

st. 
    a set of linear constraints, and
    z_i >= 0, x_i >=0, y_i >= 0   for all i

I managed to load everything into a ClpModel using a loadQuadraticObjective with the quad coefficients inserted in a CoinPackedMatrix called Q.
My problems with solveing this, I think, come from the fact that Q is not positive semi-definite (it isn't, right?), since this (quadratic part of the) objective function is _not_ non-negative for all values of the variables (including infeasible ones like x_i < 0).
My first question is: is this correct?  (Sorry for asking such a basic question..)

Let's assume that indeed this is correct and Q is indeed not positive semi-definite.
My second question then is: but what about the fact that only for (infeasible) z_i, x_i, y_i < 0 these problems occur? 
I was thinking along the lines of maybe providing Clp with a feasible solution to start with, and then the optimization would work fine?

I'm affraid I'm working horribly outside of my normal area, so please forgive my possibly ideotic questions..
Any help would be appreciated.

Regards,

Jan-Willem Goossens




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