Flow with convex separable costs: A discretization algorithm

The problem of flow optimization in a network with convex costs can be solved by discretization or, equivalently, by approaching costs by piece wise linear functions. The author describes a primal type algorithm which can solve problems with approximate functions consisting of several thousands of pieces. This method can be easily implemented by modifying a simplex program for linear network optimization. Some theoretical results and tests are presented and used for the analysis of the performances of the method, for what accuracy and quickness concerns.