Convex separable optimization is not much harder than linear optimization
Journal of the ACM (JACM)
Hidden convexity in some nonconvex quadratically constrained quadratic programming
Mathematical Programming: Series A and B
A Survey of Algorithms for Convex Multicommodity Flow Problems
Management Science
Strongly polynomial time algorithms for certain concave minimization problems on networks
Operations Research Letters
Topology design and bandwidth allocation in ATM nets
IEEE Journal on Selected Areas in Communications
Capacity and flow assignment of data networks by generalized Benders decomposition
Journal of Global Optimization
Journal of Global Optimization
Discrete capacity and flow assignment algorithms with performance guarantee
Computer Communications
Local optimality conditions for multicommodity flow problems with separable piecewise convex costs
Operations Research Letters
Hi-index | 0.00 |
This paper provides new bounds related to the global optimization of the problem of mixed routing and bandwidth allocation in telecommunication systems. The combinatorial nature of the problem, related to arc expansion decisions, is embedded in a continuous objective function that encompasses congestion and investment line costs. It results in a non-convex multicommodity flow problem, but we explore the separability of the objective function and the fact that each associated arc cost function is piecewise-convex. Convexifying each arc cost function enables the use of efficient algorithms for convex multicommodity flow problems, and we show how to calculate sharp bounds for the approximated solutions.