A Partitioned ε-Relaxation Algorithm for Separable Convex Network Flow Problems

Computational Optimization and Applications

Volumn 12, Issue 1-3, 1999, Pages 107-126

  De Leone, Renato ^a   Meyer, Robert R ^b   Zakarian, Armand ^b  

^a UNIVERSITY OF CAMERINO   (Italy)

^b University of Wisconsin Madison   (United States)

Author keywords

Asynchronous; Network flows; Relaxation methods

Indexed keywords

EID: 0007637676     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008667714641     Document Type: Article

References (13)

1. D. Bertsekas, Linear Network Optimization: Algorithms and Codes, The MIT Press: Cambridge, MA, 1991.
2. D.P. Bertsekas, RA. Hosein, and P. Tseng, "Relaxation methods for network flow problems with convex arc costs," SIAM Journal on Control and Optimization, vol. 25, pp. 1219-1243, 1987.
3. D. Bertsekas, L. Polymenakos, and R Tseng, "An ε-relaxation method for separable convex cost network flow problems," SIAM Journal on Optimization, vol. 7, pp. 953-970, 1997.
4. D. Bertsekas and J. Tsitsiklis, Parallel and Distributed Computation, Prentice Hall: Englewood Cliffs, NJ, 1989.
5. M. Collins, L. Cooper, R. Helgason, J. Kennington, and L. LeBlanc, "Solving the pipe network analysis problem using optimization techniques," Management Science, vol. 24, pp. 747-760, 1978.
6. T. Hu, "Minimum cost flows in convex cost networks," Naval Research Logistics Quarterly, vol. 13, pp. 1-9, 1966.
7. P. Kamesam and R. Meyer, "Multipoint methods for separable nonlinear networks," Mathematical Programming Study, vol. 22, pp. 185-205, 1984.
8. D. Klingman, A. Napier, and J. Stutz, "NETGEN - A program for generation of large-scale (un)capacitated assignment, transportation and minimum cost network problems," Management Science, vol. 20, pp. 814-822, 1974.
9. T. Magnanti, "Models and algorithms for predicting urban traffic equilibria," in Transportation Planning Models, M. Florian (Ed.), North-Holland: Amsterdam, 1984, pp. 153-186.
10. C. Monma and M. Segal, "A primal algorithm for finding minimum-cost flows in capacitated networks with applications," Bell System Technical Journal, vol. 61, pp. 449-468, 1982.
11. R. Rockafellar, Convex Analysis, Princeton University Press: Princeton, NJ, 1970.
12. R. Rockafellar, Network Flows and Monotropic Optimization, John Wiley: New York, 1984.
13. P. Toint and D. Tuyttens, "LSNNO: A Fortran subroutine for solving large-scale nonlinear network optimization problems," ACM Transactions on Mathematical Software, vol. 18, pp. 308-328, 1992.