Deviation Method for Piecewise Linear Functions

Piecewise linear functions are often used to solve nonlinear problems approximately. Traditional piecewise linearization approaches adopt extra binary variables to indicate which interval is activated exactly in all piecewise line segments which approximate the nonlinear problem. The number of binary variables is the essential element determining whether large size problems can be solved or not. With m line segments by m  1 break points, m extra binary variables are required in traditional methods, while the extra binary variables have been reduced to  m 2 log by Li et al. (2009). It has been accepted as the most efficient technique published to date, requiring the least number of extra binary variables. However, this study proposes a novel method to formulate piecewise linear function in which the extra binary variables are no longer required. In addition, some computational results show that the proposed model is more efficient than the method of Li et al. (2009).

Project ID:PB10309-0032
External Project ID:MOST103-2410-H182-012