Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems

Bertsekas, Dimitri P.; Tseng, Paul

doi:10.1287/opre.36.1.93

Cited by 176 publications

(87 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…One way o f avoiding the jamming problem is embodied in the R E L A X family ol serial computer codes (see [12,17,46]). Essentially, these codes make dual ascent, along directions that have a minimal number of non-zero components, which mean', that they select coordinate directions whenever possible.…”

Section: J a M M I N G And The R E L A X Approachmentioning

confidence: 99%

See 1 more Smart Citation

Dual coordinate step methods for linear network flow problems

Bertsekas

Eckstein

1988

Mathematical Programming

Self Cite

View full text Add to dashboard Cite

We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of e-complementary slackness, and most do not explicitly manipulate any "global" objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the e-relaxation algorithm for the minimum-cost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement e-relaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.

show abstract

Section: J a M M I N G And The R E L A X Approachmentioning

confidence: 99%

“…The notion of e-complementary slackness was used in [9,10], and introduced more formally in [15,17]. It was also used in the analysis of [45] (Lemma 2.2) in the special case where the flow vector f is feasible.…”

Section: E-relaxation and E-complementary Slacknessmentioning

confidence: 99%

Dual coordinate step methods for linear network flow problems

Bertsekas

Eckstein

1988

Mathematical Programming

Self Cite

View full text Add to dashboard Cite

show abstract

“…In order to illustrate the expected performance of the above parallel primal dual minimum cost network flow algorithms, we designed a synchronous and two asynchronous parallel versions of one of the primal-dual codes developed by Bertsekas and Tseng for comparison with the RELAX code (see [BeT88] for a description). We implemented these parallel primal-dual algorithms on a shared- In our implementation on the Encore MULTIMAX, the most recent flow-price pair…”

Section: Computational Resultsmentioning

confidence: 99%

“…Our results can be used to develop parallel versions of efficient minimum cost network optimization codes such as the RELAX algorithm of [BeT88].…”

Section: {Ij(ij)ea} {Il(ji)ea} Bij < Fij < Cijmentioning

confidence: 99%

Parallel primal-dual methods for the minimum cost flow problem

Bertsekas

Castañón

1993

Comput Optim Applic

Self Cite

View full text Add to dashboard Cite

In this paper we discuss the parallel asynchronous implementation of the classical primal-dual method for solving the linear minimum cost network flow problem. Multiple augmentations and price rises are simultaneously attempted starting from several nodes with possibly outdated price and flow information.The results are then merged asynchronously subject to rather weak compatibility conditions. We show that this algorithm is valid, terminating finitely to an optimal solution. We also present computational results using an Encore Multimax that illustrate the speedup that can be obtained by parallel implementation.

show abstract

“…has been replaced with alternative variants which were proven to be significantly faster such as the SUPERK algorithm of Barr et al (1974) or, as in the case of the MODSIM model, the Relax4 network flow solver of Bertsekas & Tseng (1988), which is also used in the REALM model (REALM 2006).…”

Section: Introductionmentioning

confidence: 99%

Improving real-time reservoir operation based on combining demand hedging and simple storage management rules

Ilich¹

2010

Journal of Hydroinformatics

View full text Add to dashboard Cite

A number of deterministic reservoir optimization models are capable of finding optimal basin allocation over multiple time steps simultaneously. This is commonly referred to as Multiple TimeStep Optimization (MTO). However, such solutions are predicated on perfect foreknowledge of incoming runoff over the entire simulated period (typically one year), which is not available to reservoir operators in real time, thus creating a gap between the results of MTO-based modeling and their practical use. There is no universally accepted methodology on how the results of MTO should be used to develop practical and easy-to-understand operating rules. This paper offers a simple approach to bridge this gap and suggests additional avenues for further research in this direction.

show abstract

Relaxation Methods for Minimum Cost Ordinary and Generalized Network Flow Problems

Cited by 176 publications

References 34 publications

Dual coordinate step methods for linear network flow problems

Dual coordinate step methods for linear network flow problems

Parallel primal-dual methods for the minimum cost flow problem

Improving real-time reservoir operation based on combining demand hedging and simple storage management rules

Contact Info

Product

Resources

About