Closed as fixed if next.
With quadratic expressions containing only binary variables (either in the objective or constraints), CPLEX can make an indefinite Q matrix positive semi definite by adding a diagonal to the Q matrix and subtracting a linear expression of the binaries to compensate. This can be done since the square of a binary equals the binary. However, for quadratic constraints, if there is no linear term to start with, CPLEX can crash when doing this. Problem occurs with all supported versions, including CPLEX 12.5. Expect a fix in the first fixpack for 12.5, plus any fixpacks for earlier versions. Meanwhile, turn of the presolve qpmakepsd to avoid the problem. However, this means CPLEX requires the Q matrix to positive semi definite upon input. RTC-10846 created for this. This has been fixed in CPLEX 12.5, which is now available.
Turn off the presolve qpmakepsd parameter. If the user is relying on this feature to manage an indefinite Q matrix with all binaries, the user can perform the convexification himself. This involves adding a suitably large diagonal to the Q matrix, and subtracting a linear term using the corresponding diagonal vector. The simplest values for the diagonal vectors consist of using the absolute off diagonal terms of the rows or columns of Q, whichever is larger. Better: upgrade to CPLEX 12.5 or later, which fixes this. Initial claim that 22.214.171.124 does not fix this was incorrect; this was fixed in May of 2012.
Potential crash on models with quadratic constraints containing all binary variables and no linear terms.
Upgrade to 12.5 or later.
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