The problem of optimizing higher-order pseudo-boolean functions is generally difficult.{{cn|date=June 2021}} It is always possible to reduce a higher-order function to a quadratic function which is equivalent with respect to the optimisation, problem known as "higher-order [[clique (graph theory)|clique]] reduction" (HOCR), and the result of such reduction can be optimized with QPBO. Generic methods for reduction of arbitrary functions rely on specific substitution rules and in the general case they require the introduction of auxiliary variables.<ref name="fix" /> In practice most terms can be reduced without introducing additional variables, resulting in a simpler optimization problem, and the remaining terms can be reduced exactly, with addition of auxiliary variables, or approximately, without addition of any new variable.<ref name="elc" />
