An ∈-relaxation method for separable convex cost network flow problems

SIAM Journal on Optimization

Volumn 7, Issue 3, 1997, Pages 853-870

  Bertsekas, Dimitri P ^a   Polymenakos, Lazaros C ^a   Tseng, Paul ^b  

^a USA   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Network flows; Network optimization; relaxation

Indexed keywords

EID: 0031205944     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495285886     Document Type: Article

References (38)

1. D. P. BERTSEKAS, A Distributed Algorithm for the Assignment Problems, Laboratory for Information and Decision Systems Working Paper, M.I.T., Cambridge, MA, 1979.
2. D. P. BERTSEKAS, A unified framework for minimum cost network flow problems, Math. Programming, 32 (1985), pp. 125-145.
3. D. P. BERTSEKAS, Distributed Relaxation Methods for Linear Network Flow Problems, in Proc. 25th IEEE Conference on Decision and Control, Athens, Greece, 1986, pp. 2101-2106.
4. D. P. BERTSEKAS, Distributed Asynchronous Relaxation Methods for Linear Network Flow Problems, Laboratory for Information and Decision Systems report P-1606, M.I.T., Cambridge, MA, 1986.
5. D. P. BERTSEKAS, Linear Network Optimization: Algorithms and Codes, M.I.T. Press, Cambridge, MA, 1991.
6. D. P. BERTSEKAS, An Auction/Sequential Shortest Path Algorithm for the Min Cost Flow Problem, Laboratory for Information and Decision Systems report P-2146, M.I.T., Cambridge, MA, 1992.
7. D. P. BERTSEKAS AND D. A. CASTANON, A generic auction algorithm for the minimum cost network flow problem, Comput. Optim. Appl., 2 (1993), pp. 229-260.
8. D. P. BERTSEKAS, D. CASTANON, J. ECKSTEIN, AND S. A. ZENIOS, Parallel network optimization survey, Handbooks Oper. Res. Management Sci., 7 (1995), pp. 331-339.
9. D. P. BERTSEKAS AND J. ECKSTEIN, Distributed Asynchronous Relaxation Methods for Linear Network Flow Problems, in Proc. International Federation of Automatic Control '87, Munich, Germany, July 1987.
10. D. P. BERTSEKAS AND J. ECKSTEIN, Dual coordinate step methods for linear network flow problems, Math. Programming, 42 (1988), pp. 203-243.
11. D. P. BERTSEKAS AND D. EL BAZ, Distributed asynchronous relaxation methods for convex network flow problems, SIAM J. Control Optim., 25 (1987), pp. 74-85.
12. D. P. BERTSEKAS, P. A. HOSEIN, AND P. TSENG, Relaxation methods for network flow problems with convex arc costs, SIAM J. Control Optim., 25 (1987), pp. 1219-1243.
13. D. P. BERTSEKAS AND P. TSENG, Relaxation methods for minimum cost ordinary and generalized network flow problems, Oper. Res., 36 (1988), pp. 93-114.
14. D. P. BERTSEKAS AND P. TSENG, RELAX-IV: A Faster Version of the RELAX Code for Solving Minimum Cost Flow Problems, Laboratory for Information and Decision Systems report P-2276, M.I.T., Cambridge, MA, 1994.
15. D. P. BERTSEKAS AND J. N. TSITSIKLIS, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1989.
16. R. G. BLAND AND D. L. JENSEN, On the computational behavior of a polynomial-time network flow algorithm, Math. Programming, 54 (1992), pp. 1-39.
17. R. DE LEONE, R. R. MEYER, AND A. ZAKARIAN, An ∈-Relaxation Algorithm for Convex Network Flow Problems, Computer Sciences Department Technical report, University of Wisconsin, Madison, WI, 1995.
18. J. EDMONDS AND R. M. KARP, Theoretical improvements in algorithmic efficiency for network flow problems, J. Assoc. Comput. Mach., 19 (1972), pp. 248-264.
19. L. R. FORD, JR., AND D. R. FULKERSON, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
20. A. V. GOLDBERG AND R. E. TARJAN, Solving minimum cost flow problems by successive approximation, Math. Oper. Res., 15 (1990), pp. 430-466.
21. A. V. GOLDBERG, Efficient Graph Algorithms for Sequential and Parallel Computers, Laboratory for Computer Science Technical report TR-374, M.I.T., Cambridge, MA, 1987.
22. W. W. HAGER, The dual active set algorithm, in Advances in Optimization and Parallel Computing, P. M. Pardalos, ed., North-Holland, Amsterdam, the Netherlands, 1992, pp. 137-142.
23. W. W. HAGER AND D. W. HEARN, Application of the dual active set algorithm to quadratic network optimization, Comput. Optim. Appl., 1 (1993), pp. 349-373.
24. P. V. KAMESAM AND R. R. MEYER, Multipoint methods for separable nonlinear networks, Math. Programming Study, 22 (1984), pp. 185-205.
25. A. V. KARZANOV AND S. T. MCCORMICK, Polynomial methods for separable convex optimization in unimodular linear spaces with applications to circulations and co-circulations in network, SIAM J. Comput., 26 (1997), pp. 1248-1278.
26. D. KLINGMAN, A. NAPIER, AND J. STUTZ, NETGEN - A program for generating large scale (un) capacitated assignment, transportation, and minimum cost flow network problems, Management Sci., 20 (1974), pp. 814-822.
27. X. LI AND S. A. ZENIOS, Data Parallel Solutions of Min-Cost Network Flow Problems Using ∈-Relaxations, Department of Decision Sciences report 1991-05-20. University of Pennsylvania, Philadelphia, PA, 1991.
28. R. R. MEYER, Two-segment separable programming, Management Sci., 25 (1979), pp. 285-295.
29. S. S. NIELSEN AND S. A. ZENIOS, On the massively parallel solution of linear network flow problems, in Network Flow and Matching: First DIMACS Implementation Challenge, D. Johnson and C. McGeoch, eds., American Mathematical Society, Providence, RI, 1993, pp. 349-369.
30. L. C. POLYMENAKOS, Parallel shortest path auction algorithms, Parallel Comput., 20 (1994), pp. 1221-1247.
31. L. C. POLYMENAKOS, ∈-Relaxation and Auction Algorithms for the Convex Cost Network Flow Problem, Electrical Engineering and Computer Science Department Ph.D. the sis, M.I.T., Cambridge, MA, 1995.
32. H. RÖCK, Scaling techniques for minimal cost network flows, in Discrete Structures and Algorithms, U. Pape and Carl Hanser, eds., München, Germany, 1980, pp. 181-191.
33. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
34. R. T. ROCKAFELLAR, Network Flows and Monotropic Programming, Wiley-Interscience, New York, NY, 1984.
35. P. TSENG, Relaxation Methods for Monotropic Programming Problems, Operations Research Center Ph.D. thesis, M.I.T., Cambridge, MA, 1986.
36. P. TSENG, D. P. BERTSEKAS, AND J. N. TSITSIKLIS, Partially asynchronous, parallel algorithms for network flow and other problems, SIAM J. Control Optim., 28 (1990), pp. 678-710.
37. J. A. VENTURA, Computational development of a lagrangian dual approach for quadratic networks, Networks, 21 (1991), pp. 469-485.
38. A. WEINTRAUB, A primal algorithm to solve network flow problems with convex costs, Management Sci., 21 (1974), pp. 87-97.