Optimal scaling of a gradient method for distributed resource allocation

Journal of Optimization Theory and Applications

Volumn 129, Issue 3, 2006, Pages 469-488

  Xiao, L ^a   Boyd, S ^b  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b Stanford University   (United States)

Author keywords

Convergence rates; Distributed optimization; Resource allocations; Semidefinite programming; Weighted gradient methods

Indexed keywords

COST FUNCTIONS; GRADIENT METHODS; LINEAR MATRIX INEQUALITIES;

CONDITION; CONVERGENCE RATES; DISTRIBUTED OPTIMIZATION; DISTRIBUTED RESOURCE ALLOCATION; GRADIENT'S METHODS; LOCAL VARIABLES; RESOURCES ALLOCATION; SCALINGS; SEMI-DEFINITE PROGRAMMING; WEIGHTED GRADIENT METHOD;

RESOURCE ALLOCATION;

EID: 33747317125     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-006-9080-1     Document Type: Article

References (26)

1. ARROW, K. J., and HURWICZ, L., Decentralization and Computation in Resource Allocation, Essays in Economics and Econometrics, Edited by R. W. Pfouts, University of North Carolina Press, Chapel Hill, North Carolina, pp. 34-104, 1960.
2. HEAL, G. M., Planning without Prices, Review of Economic Studies, Vol. 36, pp. 347-362, 1969.
3. KUROSE, J. F., and SIMHA, R., A Microeconomic Approach to Optimal Resource Allocation in Distributed Computer Systems, IEEE Transactions on Computers, Vol. 38, pp. 705-717, 1989.
4. BERTSEKAS, D. P., Nonlinear Programming, 2nd Edition, Athena Scientific, Belmont, Massachusetts, 1999.
5. BOYD, S., and VANDENBERGHE, L., Convex Optimization, Cambridge University Press, Cambridge, UK, 2004.
6. HURWICZ, L., The Design of Mechanisms for Resource Allocation, American Economic Review, Vol. 63, pp. 1-30, 1973.
7. Ho, Y. C., SERVI, L. D., and SURI, R., A Class of Center-Free Resource Allocation Algorithms, Large Scale Systems, Vol. 1, pp. 51-62, 1980.
8. SERVI, L. D., Electrical Networks and Resource Allocation Algorithms, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 10, pp. 841-848, 1980.
9. ROCKAFELLAR, R. T., Network Flows and Monotropic Optimization, John Wiley and Sons, New York, NY, 1984.
10. BERTSEKAS, D. P., and TSTTSIKLIS, J. N., Parallel and Distributed Computation, Prentice-Hall, Englewood, Cliffs, New Jersey, 1989.
11. BERTSEKAS, D. P., Network Optimization: Continuous and Discrete Models, Athena Scientific, Belmont, Massachusetts, 1998.
12. TSITSIKLIS, J. N., and BERTSEKAS, D. P., Distributed Asynchronous Optimal Routing in Data Networks, IEEE Transactions on Automatic Control, Vol. 31, pp. 325-332, 1986.
13. EL BAZ, D., Asynchronous Gradient Algorithms for a Class of Convex Separable Network Flow Problems, Computational Optimization and Applications, Vol. 5, pp. 187-205, 1996.
14. LUO, Z. Q., and TSENG, P., On the Rate of Convergence of a Distributed Asynchronous Routing Algorithm, IEEE Transactions on Automatic Control, Vol. 39, pp. 1123-1129, 1994.
15. TSITSIKLIS, J. N., BERTSEKAS, D. P., and ATHANS, M., Distributed Asynchronous Deterministic and Stochastic Gradient Optimization Algorithms, IEEE Transactions on Automatic Control, Vol. 31, pp. 803 812, 1986.
16. BOYD, S., DIACONIS, P., and XIAO, L., Fastest Mixing Markov Chain on a Graph, SIAM Review, Vol. 46, pp. 667-689, 2004.
17. XIAO, L., and BOYD, S., Fast Linear Iterations for Distributed Averaging, Systems and Control Letters, Vol. 53, pp. 66-78, 2004.
18. HORN, R. A., and JOHNSON, C. A., Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
19. METROPOLIS, N., ROSENBLUTH, A., ROSENBLUTH, M., TELLER, A., and TELLER, E., Equations of State Calculations by Fast Computing Machines, Journal of Chemical Physics, Vol. 21, pp. 1087-1092, 1953.
20. DIACONIS, P., and SALOFF-COSTE, L., What Do We Know About the Metropolis Algorithms, Journal of Computer and System Sciences, Vol. 57, pp. 20-36, 1998.
21. VANDENBERGHE, L., and BOYD, S., Semidefinite Programming, SIAM Review, Vol. 38, pp. 49-95, 1996.
22. NESTEROV, Y., and NEMIROVSKII, A., Interior-Point Polynomial Algorithms in Convex Programming, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pennsylvania, 1994.
23. Ye, Y., Interior-Point Algorithms: Theory and Analysis, John Wiley and Sons, New York, NY, 1997.
24. WOLKOWICZ, H., SAIGAL, R., and VANDENGERGHE, L., Editors, Handbook of Semidefinite Programming: Theory, Algorithms, and Applications, Kluwer Academic Publishers, Boston, Massachusetts, 2000.
25. MERRIS, R., Laplacian Matrices of Graphs: A Survey, Linear Algebra and Its Applications, Vol. 197, pp. 143-176, 1994.
26. GODSIL, C., and ROYLE, G., Algebraic Graph Theory, Springer, New York, NY, 2001.