The authors consider the problem of maximizing the product \(l_1(x)l_2(x)\) of two linear functions \(l_1(x)\) and \(l_2(x)\) where \(x\in \{0,1\}^n\) is a discrete variable or a continuous variable with \(0\leq x\leq 1\).
Linear and low-order polynomial algorithms are given for the continuous problem. Furthermore, penalties are described for the discrete problem. Numerical tests are given.