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Abstract: We propose two new methods for the solution of the single commodity, separable convex cost network flow problem: the #-relaxation method and the auction/sequential shortest path method. Both methods were originally developed for linear cost problems and reduce to their linear conterparts when applied to such problems. We show that both methods stem from a common algorithmic framework, that they terminate with a near optimal solution, and we provide an associated complexity analysis. We also... (Update)
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BibTeX entry: (Update)
@misc{ bertsekas-epsilonrelaxations,
author = "Dimitri P. Bertsekas and Lazaros C. Polymenakos and Paul Tseng",
title = "ε-Relaxations and Auction Methods for Separable Convex Cost Network
Flow Problems",
url = "citeseer.ist.psu.edu/bertsekas96epsilonrelaxations.html" }
Citations (may not include all citations):640 Princeton University Press (context) - Rockafellar - 1970
348 Parallel and Distributed Computation: Numerical Methods (context) - Bertsekas, Tsitsiklis - 1989
303 Princeton University Press (context) - Ford, Jr - 1962
47 Linear Network Optimization: Algorithms and Codes (context) - Bertsekas - 1991
34 Solving Minimum Cost Flow Problems by Successive Approximati.. (context) - Goldberg, Tarjan - 1990
27 Theoretical Improvements in Algorithmic E#ciency for Network.. (context) - Edmonds, Karp - 1972
14 Relaxation Methods for Minimum Cost Ordinary and Generalized.. (context) - Bertsekas, Tseng - 1988
12 Dual Coordinate Step Methods for Linear Network Flow Problem.. - Bertsekas, Eckstein - 1988
11 Relaxation Methods for Network Flow Problems with Convex Arc.. (context) - Bertsekas, Hosein et al. - 1987
10 Network Flows and Monotropic Programming (context) - Rockafellar - 1984
10 Distributed Asynchronous Relaxation Methods for Linear Netwo.. (context) - Bertsekas - 1986
10 Distributed Asynchronous Relaxation Methods for Linear Netwo.. (context) - Bertsekas, Eckstein - 1987
7 Partially Asynchronous, Parallel Algorithms for Network Flow.. (context) - Tseng, Bertsekas et al. - 1990
7 Polynomial Methods for Separable Convex Optimization in Unim.. - Karzanov, McCormick - 1993
7 Scaling Techniques for Minimal Cost Network Flows (context) - Rock - 1980
[Article contains additional citations not shown here]
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