Fenchel duality and smoothness of solution of the optimal routing problem (Q1080359)

A particular dynamic, linear state and control constrained optimization problem arising in optimal routing in communication networks is investigated by Fenchel duality methods. The original problem is shown to reduce to a finite dimensional dual program having a fairly simple solution. In particular, it is shown that an optimal solution always exists having the following property: all state trajectory components have constant slopes until they switch to zero, whenever the corresponding component hits the boundary. Implications of the main results for the development of on-line solution algorithms are discussed and possible extensions are outlined. The paper concentrates on aspects interesting to control theorists and gives references including important extensions of communication network applications.