Network design applications of the class of column generation/simplicial decomposition algorithms in convex differentiable optimization

A new class of column generation/simplicial decomposition method for non linear convex and differentiable programming is presented. The new algorithm class builds on the intuitively appealing idea that non linear column generation problems may be advantageous computationally. Different applications of this methodology are presented, with special attention to the unicommodity and multicommodity network flow problems, which are obtained when some decomposition methods applied to network design problems.