Restricted Simplicial Decomposition for Symmetric Convex Cost Flow Problems

This paper presents a variation of the restricted simplicial decomposition (RSD) algorithm especially designed for solving nonlinear network problems with unrestricted arc flows and an objective function that is separable, strictly convex and symmetric with respect to the origin. These problems have the drawback that the standard linear subproblem of RSD is unbounded. However, their optimal solution is in the convex hull of a set of spanning tree solutions. The proposed algorithm uses a new linearized subproblem with nonnegative arc costs in a directed network, thereby avoiding negative cycles and guaranteeing the generation of a spanning treeat each iteration. Computational results are presented for some large-scale electrical networks and water distribution problems.