Efficient minimization over products of simplices and its application to nonlinear multicommodity network problems

Many problems in portfolio selection, in traffic planning and in computer communication networks can be formulated as nonlinear problems involving minimization of a nonlinear function over simplices. Based on the concepts of regularization and partial linearization, we propose an efficient solution technique for such programs, prove its global convergence and discuss the possibilities for parallel implementation. We provide, as an application, an algorithm for traffic assignment which outperforms previous state-of-the-art codes.