Originally posted by: SystemAdmin
[jfk said:]
Hello,
I suppose you are solving a quadratic problem.
in the manual under
User's Manual > ILOG CPLEX User's Manual > Continuous optimization > Solving problems with quadratic constraints (QCP) > Identifying a quadratically constrained program (QCP)
you can find what types of quadratic programs CPLEX can solve: "The constraints must each define a convex region. To make sure of convexity, ILOG CPLEX requires that each Q i matrix be positive semi-definite (PSD) or that the constraint can be transformed into a second order cone"
apparently your Q (the quadratic part) is not positive semi-definite.
convexity is a very important feature of a problem. When it doesn't have it all sort of problems will occur because the basic lemmas and theorems for most (if not all) algorithms don't hold. What I have read in the literature usually they try to cover the possible region with a convex hull and solve that then repair the solution if it is necessary or cut the region into smaller, convex pieces and solve the resulting problems separately but they always go back somehow to convexity. So it seems to me that the only way to solve this issue is to make your quadratic constraints (the Q) positive semi-definite.
I hope it helps
cheers
#DecisionOptimization#OPLusingCPLEXOptimizer