Originally posted by: GlcBrero

Hi All,

I am using using Cplex Optimization Studio 12.8 to solve a non-convex quadratic programming problem with integer variables.

According to the instructions at this link "https://www.ibm.com/support/knowledgecenter/ru/SSSA5P_12.7.1/ilog.odms.cplex.help/CPLEX/Parameters/topics/OptimalityTarget.html", I know I need to set the optimality target to 3 to avoid Error 5002 (CPXERR_Q_NOT_POS_DEF) . However, if I only consider boolean variables, I can solve the problem with the standard optimality target.

Which algorithm is Cplex using to solve a non-convex quadratic programming problem with boolean variables?

Thank you very much!

Gianluca

Just guessing, but CPLEX might linearize the problem (which you can always do when all variables are boolean) and then solver an ILP model.

Originally posted by: PierreBonami

Hi,

Yes one possibility when all products involve at least one boolean variable is to linearize the products. Another one when you only have products of binary variables is to convexify the model. Both approaches are explained with a bit more details for example here (Section 2) with some discussions on the advantages/disadvantages (in Section 3):
http://cerc-datascience.polymtl.ca/wp-content/uploads/2018/01/Technical-Report_DS4DM-2017-013.pdf

Best regards,

Pierre