Distributed subgradient methods for multi-agent optimization

IEEE Transactions on Automatic Control

Volumn 54, Issue 1, 2009, Pages 48-61

  Nedić, Angelina ^a   Ozdaglar, Asuman ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b Massachusetts Institute of Technology ^*  (United States)

Author keywords

Convex optimization; Cooperative control; Distributed optimization; Multi agent network; Subgradient method

Indexed keywords

AGENTS; CONVEX OPTIMIZATION; MULTI AGENT SYSTEMS; PROBABILITY DENSITY FUNCTION; TIME VARYING NETWORKS;

CONVERGENCE RATES; CONVERGENCE RESULTS; CONVEX OBJECTIVES; COOPERATIVE CONTROL; DISTRIBUTED COMPUTATIONS; DISTRIBUTED OPTIMIZATION; MULTI AGENTS; MULTI-AGENT NETWORK; MULTIPLE AGENTS; NUMBER OF ITERATIONS; OBJECTIVE FUNCTIONS; OPTIMAL SOLUTIONS; OPTIMIZATION PROBLEMS; SUBGRADIENT METHOD; TIME-VARYING;

OPTIMIZATION;

EID: 59649103668     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.2009515     Document Type: Article

References (25)

1. J. N. Tsitsiklis, "Problems in Decentralized Decision Making and Computation," Ph.D. dissertation, Dept. Elect. Eng. Comp. Sci., Massachusetts Institute of Technology, Cambridge, 1984.
2. J. N. Tsitsiklis, D. P. Bertsekas, and M. Athans, "Distributed asynchronous deterministic and stochastic gradient optimization algorithms," IEEE Trans. Automat. Control, vol. AC-31, no. 9, pp. 803-812, Sep. 1986.
3. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods. Belmont, MA: Athena Scientific, 1997.
4. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Schochet, "Novel type of phase transitions in a system of self-driven particles," Phys. Rev. Lett., vol. 75, no. 6, pp. 1226-1229, 1995.
5. A. Jadbabaie, J. Lin, and S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Automat. Control, vol. 48, no. 6, pp. 988-1001, Jun. 2003.
6. S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, "Gossip algorithms: Design, analysis, and applications," in Proc. IEEE INFOCOM, 2005, pp. 1653-1664.
7. R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Automat. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
8. M. Cao, D. A. Spielman, and A. S. Morse, "A lower bound on convergence of a distributed network consensus algorithm," in Proc. IEEE CDC, 2005, pp. 2356-2361.
9. A. Olshevsky and J. N. Tsitsiklis, "Convergence rates in distributed consensus averaging," in Proc. IEEE CDC, 2006, pp. 3387-3392.
10. A. Olshevsky and J. N. Tsitsiklis, "Convergence Speed in Distributed Consensus and Averaging," Massachusetts Institute of Technology, Cambridge, 2006.
11. F. P. Kelly, A. K. Maulloo, and D. K. Tan, "Rate control for communication networks: Shadow prices, proportional fairness, and stability," J. Oper. Res. Soc., vol. 49, pp. 237-252, 1998.
12. S. Low and D. E. Lapsley, "Optimization flow control, I: Basic algorithm and convergence," IEEE/ACM Trans. Networking, vol. 7, no. 6, pp. 861-874, Dec. 1999.
13. R. Srikant, Mathematics of Internet Congestion Control. Boston, MA: Birkhauser, 2004.
14. M. Chiang, S. H. Low, A. R. Calderbank, and J. C. Doyle, "Layering as optimization decomposition: A mathematical theory of network architectures," Proc. IEEE, vol. 95, no. 1, pp. 255-312, Jan. 2007.
15. D. P. Bertsekas, A. Nedić, and A. E. Ozdaglar, Convex Analysis and Optimization. Cambridge, MA: Athena Scientific, 2003.
16. V. D. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis, "Convergence in multiagent coordination, consensus, and flocking," in Proc. IEEE CDC, 2005, pp. 2996-3000.
17. A. Nedić and A. Ozdaglar, "Convergence Rate for Consensus with Delays," J. Global Optim., pp. 1-23, Oct. 2007.
18. N. Z. Shor, Minimization Methods for Nondifferentiable Functions Transl.:fRom Russian by K.C. Kiwiel and A. Ruszczynski. Berlin, Germany: Springer, 1985.
19. B. T. Polyak, Introduction to Optimisation. New York: Optimization Software, Inc., 1987.
20. A. Nedić and D. P. Bertsekas, "Convergence rate of incremental subgradient algorithms," in Stochastic Optimization: Algorithms and Applications, S. Uryasev and P. Pardalos, Eds. Norwell, MA: Kluwer Academic, 2000.
21. A. Nedić and D. P. Bertsekas, "Incremental subgradient methods for nondifferentiable optimization," SIAM J. Optim., vol. 56, no. 1, pp. 109-138, 2001.
22. A. Nedić, D. P. Bertsekas, and V. S. Borkar, "Distributed asynchronous incremental subgradient methods," in Inherently Parallel Algorithms in Feasibility and Optimization and their Applications, D. Butnariu, Y. Censor, and S. Reich, Eds. New York: Elsevier, 2001.
23. A. Nedić and A. Ozdaglar, "Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods," Massachusetts Institute of Technology, Cambridge, 2007.
24. A. Kashyap, T. Basar, and R. Srikant, "Quantized consensus," in Proc. IEEE CDC, 2006, pp. 635-639.
25. R. Carli, F. Fagnani, A. Speranzon, and S. Zampieri, "Communication constraints in coordinated consensus problems," in Proc. IEEE ACC 2006, pp. 1-6.