A Superior Representation Method for Piecewise Linear Functions

Authors:
Han-Lin Li;Hao-Chun Lu;Chia-Hui Huang;Nian-Ze Hu
Affiliations:
Institute of Information Management, National Chiao Tung University, Hsinchu 300, Taiwan;Department of Information Management, Fu Jen Catholic University, Taipei 242, Taiwan;Department of Information Management, Kainan University, Taoyuan 33857, Taiwan;Department of Information Management, National Formosa University, Yunlin 632, Taiwan
Venue:
INFORMS Journal on Computing
Year:
2009

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Abstract

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.