A Superior Representation Method for Piecewise Linear Functions

Many nonlinear programs can be piecewisely linearized by adding extra binary variables. For the last four decades, several techniques of formulating a piecewise linear function have been developed. By expressing a piecewise linear function with m + 1 break points, the current method requires us to use m additional binary variables and 4m constraints, which causes heavy computation when m is large. This study proposes a superior way of expressing the same piecewise linear function, where only ⌈ log 2m ⌉ binary variables and 8 + 8 ⌈ log 2m ⌉ additive constraints are used. Various numerical experiments demonstrate that the proposed method is more computationally efficient than current methods.