A proposition to exploit the partially linear structure of the nonlinear multicommodity flow optimization problem

Optimization problems arising in telecommunications are often large-scale nonlinear problems. Usually their big size is generated mainly by their linear parts but the existence of small or medium nonlinear parts prevents us from directly tackling them with linear solvers, which are efficient. Instead, the author has proposed a method to decompose big nonlinear problems into nonlinear and linear parts. Its coordination procedure uses two auxiliary solvers: quadratic and pure nonlinear. The procedure falls in the class of projection methods. Special cuts proposed by the author allow to avoid an excessive zigzagging while not enormously increasing the complexity of both the parts. The validity of these cuts can be analyzed within the framework of obtuse cone model. Here the author summarizes the method and analyses its applicability to nonlinear multicommodity flow problems. The structure and particular sizes of this problem make the method useful. The considerations are illustrated by a numerical example with a multicommodity flow problem