0-1 non convex quadratic problem in CPLEX

Question

Can CPLEX solve non-convex 0-1 quadratic optimization problem? If so, does anyone know how?

Answer 1

Note that a $0$-$1$ quadratic function of $x=(x_1,\dots,x_n)$ can always be made convex by adding a sufficiently large multiple of $\sum_i (x_i^2-x_i)$, which is $0$ for binary $x$.

Alternatively, you can linearize a binary quadratic objective by introducing a binary (or just nonnegative) variable $y_{i,j}$ to represent $x_i x_j$, along with linear constraints: \begin{align} y_{i,j} &\le x_i \\ y_{i,j} &\le x_j \\ y_{i,j} &\ge x_i + x_j - 1 \end{align}

I don't know whether CPLEX does either of these transformations automatically, but you can do it yourself before calling the solver.