On solving a nondifferentiable nonlinear transshipment problem

The paper presents a new type of transshipment problem with a nonseparable nonlinear function, such that each variable can be expressed by a piecewise nonlinear function of the arc flow. The algorithm for dealing with the nondifferentiable part is described; it uses the environment defined by partitioning the set of variables in basic and nonbasic. Since a maximal basis is assumed, the treatment of the nondifferentiable part is only required while de-activating nonbasic variables; at this point, first-order information is used and the concept of up and down Lagrange multipliers is introduced. A mechanism for blocking the de-activation of some nonbasic variables is described. Some computational experience obtained while testing the new approach on real-world problems is reported.