A sequential simplex algorithm for the continuous convex piecewise linear network flow problem

Abstract

This paper presents a descent algorithm for the continuous convex piecewise linear network flow problem (CCPWLNFP). The CCPWLNFP can be reformulated as a linear programming problem and directly solved by mature algorithms. However, reformulation methods not only greatly increase the problem scale but also destroy the excellent structure of the constraint matrix. The sequential simplex algorithm (SSA) makes use of the linearity of the cost function on each segment and transforms the CCPWLNFP to a series of linear network flow problems with the original constraint matrix. The mature bounded network simplex algorithm can be applied to solve these linear network flow problems efficiently. In numerical experiments, the SSA is compared with two reformulation methods and shows its superior optimization efficiency.