Do CPLEX or Gurobi handle MIQPs with indefinite coefficient matrices?
The problem I am dealing with has quadratic terms in which one variable is binary and the other variable is continuous. The coefficient matrix of the quadratic form is far from positive semi-definite. Its entries are data-dependent. Thus, I have no control over the positive semi-definiteness.
Can CPLEX or Gurobi handle such models at all? Note that it's a MIQP with binary variables and continuous variables, not a QP.
Is there other software for such problems?
What is the state of the art, algorithmically?