Relaxation methods for network flow problems with convex arc costs
SIAM Journal on Control and Optimization
Parallel and distributed computation: numerical methods
Parallel and distributed computation: numerical methods
Linear network optimization: algorithms and codes
Linear network optimization: algorithms and codes
LSNNO, a FORTRAN subroutine for solving large-scale nonlinear network optimization problems
ACM Transactions on Mathematical Software (TOMS)
An $\epsilon$-Relaxation Method for Separable Convex Cost Network Flow Problems
SIAM Journal on Optimization
Journal of Optimization Theory and Applications
Minimum-cost multicast over coded packet networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
A proximal subgradient projection algorithm for linearly constrained strictly convex problems
Optimization Methods & Software
Projected Perspective Reformulations with Applications in Design Problems
Operations Research
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A relaxation method for separable convex network flowproblems is developed that is well-suited for problems withlarge variations in the magnitude of the nonlinear cost terms.The arcs are partitioned into two sets, one of which containsonly arcs corresponding to strictly convex costs. The algorithmadjusts flows on the other arcs whenever possible, andterminates with primal-dual pairs that satisfy complementaryslackness on the strictly convex arc set and ε-complementaryslackness on the remaining arcs. An asynchronous parallelvariant of the method is also developed. Computational resultsdemonstrate that the method is significantly more efficient onill-conditioned networks than existing methods, solving problemswith several thousand nonlinear arcs in one second or less.