Originally posted by: SystemAdmin

Hi,
In a genome wide association study, I need to solve a quadratic programming problem with 500,000 variables.
Is CPLEX able to handle a problem of this size, if not, what is the largest quadratic programming problem that CPLEX can handle.
I am using a Linux machine with 16 cores and 64 GB of memory.

Thanks for your help in advance.
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Originally posted by: SystemAdmin

CPLEX does not have any hard-coded limits on the number of variables or constraints. Variables and constraints are indexed by 32bit signed integers, so you cannot have more than 2^31-1 of them.
Is this QP you want to solve a continuous problem or does it involve integer variables?
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Originally posted by: SystemAdmin

Thanks for your reply. My QP is a continuous problem.
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Originally posted by: T_O

You should also remember that your problem has to be convex (if I remember correctly).
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Originally posted by: Christian Bliek

Yes, cplex can solve such large models if they are sparse. For qp the q matrix should be sparse as well.

In some models the q matrix is in fact the product of two sparse matrices q = p'p. If that is the case, it is better to avoid doing this multiplication because it might lead to a dense q, but reformulate the model instead. E.g. replace x'p'px by y'y and add the constraint y = px.

Since release 12.3 we can handle both convex and non-convex qp. If it is not convex you need to set the solution target parameter to 2 and you will obtain a kkt point. Note however that solving non-convex qp is significantly harder than solving convex qp and is therefore likely to take more time.

Christian.
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