Applications of Simplicial Decomposition with Nonlinear Column Generation to Nonlinear Network Flows

Abstract

The simplicial decomposition method for linearly constrained nonlinear programs has been proven to be efficient for certain classes of structured large-scale problems. This method alternates between a multi-dimensional search over a restriction of the feasible set and an augmentation of the restriction through the solution of a linear column generation problem. The quality of the columns generated may however be very poor, since the first-order approximation of the objective function is used globally.