Originally posted by: EdKlotz
>
> Greetings, I have two concrete questions I need help with:
>
> 1. I have a set of quadratic constraints of the form xTCx + ATx <= P (T is
> transpose), where in this case C is NOT positive semi-definite, A is a vector
> of non-negative parameters and P is a constant. Nonetheless, when I submit the
> problem to CPLEX (12.4.0.1), it can solve it (reports a solution). My concrete
> question is, why is this happening?, doesn't CPLEX require for the C matrix to
> be positive semi-definite, or is it handling the non-convexity somehow?
>
If the x variables are binary, this is to be expected. CPLEX can then
convexify the indefinite C matrix by adding a multiple of the square of each
binary while subtracting a linear multiple of the same binary (i.e. because
x^2 = x for binary variables).
Note that this only requires that some of the x variables are binary,
provided that the indefiniteness is associated with the binary variables
rather than the others.
Otherwise, I would not expect this with quadratic constraints. In such
a case, I would suggest that you confirm that your matrix really is indefinite.
If you want help with this, can you provide a representation of the matrix
and a submatrix that proves indefiniteness? Note that you can download a
program that will do this for quadratic objectives at:
http://www-01.ibm.com/support/docview.wss?uid=swg21400047 > 2. Can CPLEX handle MISOCP's? Does it require a specific format (for example if using AMPL)
Yes it does. Just specify the second order cone constraints, either
directly or as rotated cones. I had a quick look at the AMPL web page
and the solver interface to CPLEX, and it appears to support passing
second order cones to CPLEX.
>
> Thank you so much,
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