A dual simplex algorithm for piecewise-linear programming

This paper presents a dual piecewise-linear simplex algorithm for minimizing convex separable piecewise-linear functions subject to linear constraints. It is an extension of Fourier’s work on piecewise-linear programming to the dual piecewise-linear simplex algorithm. This algorithm has advantages over indirect methods which solve equivalent linear programs augmented by additional variables and/or constraints. Computational experience is presented which demonstrates the efficiency these advantages contribute.