Fenchel duality and smoothness of solution of the optimal routing problem
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.
scientific article; zbMATH DE number 3965790
scientific article