Multiuser optimization: Distributed algorithms and error analysis

SIAM Journal on Optimization

Volumn 21, Issue 3, 2011, Pages 1046-1081

  Koshal, Jayash ^a   Nedić, Angelia ^a   Shanbhag, Uday V ^a  

^a United States of America   (United States)

Author keywords

Convex optimization; Distributed optimization; Gradient methods; Multiuser optimization; Projection methods; Variational inequalities

Indexed keywords

CONGESTED TRAFFIC NETWORKS; CONSTRAINED OPTIMIZATION PROBLEMS; COUPLING CONSTRAINTS; DECISION VARIABLES; DISTRIBUTED OPTIMIZATION; DUAL SPACES; ERROR BOUND; FIXED NUMBERS; GRADIENT BASED; LINEAR CONSTRAINTS; MULTI-USER; NONLINEAR COUPLING; OPTIMAL FUNCTION; OPTIMIZATION PROBLEMS; PRIMAL-DUAL; PROJECTION METHOD; REGULARIZATION PARAMETERS; STEP LENGTH; TIKHONOV REGULARIZATION; UTILITY FUNCTIONS; VARIATIONAL INEQUALITIES;

APPROXIMATION ALGORITHMS; CONSTRAINED OPTIMIZATION; CONVEX OPTIMIZATION; ERROR ANALYSIS; GRADIENT METHODS; PARAMETERIZATION; VARIATIONAL TECHNIQUES;

PROBLEM SOLVING;

EID: 80054752546     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/090770102     Document Type: Article

References (30)

1. A. BECK AND M. TEBOULLE, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2 (2009), pp. 183-202.
2. A. BECK AND M. TEBOULLE, Gradient-based algorithms with applications to signal-recovery problems, in Convex Optimization in Signal Processing and Communications, Y. Eldar and D. Palomar, eds., Cambridge University Press, Cambridge, UK, 2010, pp. 42-88.
3. D. P. BERTSEKAS, Nonlinear Programming, Athena Scientific, Belmont, MA, 1999.
4. D. P. BERTSEKAS, A. NEDIĆ, AND A. OZDAGLAR, Convex Analysis and Optimization, Athena Scientific, Belmont, MA, 2003.
5. D. P. BERTSEKAS AND J. TSITSIKLIS, Parallel and Distributed Computation: Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1989.
6. R. H. BYRD, M. E. HRIBAR, AND J. NOCEDAL, An interior point algorithm for large-scale nonlinear programming, SIAM J. Optim., 9 (1999), pp. 877-900. (Pubitemid 129489310)
7. M. CHIANG, S. LOW, A. CALDERBANK, AND J. DOYLE, Layering as optimization decomposition: A mathematical theory of network architectures, Proc. IEEE, 95 (2007), pp. 255-312.
8. F. FACCHINEI AND J.-S. PANG, Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols. 1 and 2, Springer-Verlag, New York, 2003.
9. F. KELLY, A. MAULLOO, AND D. TAN, Rate control for communication networks: Shadow prices, proportional fairness, and stability, J. Oper. Res. Soc., 49 (1998), pp. 237-252. (Pubitemid 128610018)
10. I. V. KONNOV, Equilibrium Models and Variational Inequalities, Math. Sci. Eng. 210, Elsevier B.V., Amsterdam, 2007.
11. I. KONNOV, Equilibrium Models and Variational Inequalities, Elsevier, New York, 2007.
12. G. M. KORPELEVICH, The extragradient method for finding saddle points and other problems, Ekonom. i Mat. Metody, 12 (1976), pp. 747-756.
13. S. LOW AND D. LAPSLEY, Optimization flow control, I: Basic algorithm and convergence, IEEE/ACM Trans. Netw., 7 (1999), pp. 861-874.
14. A. NEDIĆ AND A. OZDAGLAR, Subgradient methods in network resource allocation: Rate analysis, in Proceedings of the 42nd Annual Conference on Information Sciences and Systems, CISS, Princeton, NJ, 2008, pp. 1189-1194.
15. A. NEDIĆ AND A. OZDAGLAR, Approximate primal solutions and rate analysis for dual subgradient methods, SIAM J. Optim., 19 (2008), pp. 1757-1780.
16. A. NEDIĆ AND A. OZDAGLAR, Subgradient methods for saddle-point problems, J. Optim. Theory Appl., 142 (2009), pp. 205-228.
17. A. NEMIROVSKI, Prox-method with rate of convergence O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems, SIAM J. Optim., 15 (2004), pp. 229-251. (Pubitemid 40360669)
18. Y. NESTEROV, Smooth minimization of non-smooth functions, Math. Program., Ser. A, 103 (2005), pp. 127-152. (Pubitemid 40537674)
19. Y. NESTEROV, Dual extrapolation and its applications to solving variational inequalities and related problems, Math. Program., 109 (2007), pp. 319-344. (Pubitemid 46197859)
20. J.-S. PANG AND D. CHAN, Iterative methods for variational and complementarity problems, Math. Program., 24 (1982), pp. 284-313. (Pubitemid 13475994)
21. B. T. POLYAK, Introduction to Optimization, Transl. Ser. Math. Engrg., Optimization Software, New York, 1987.
22. X. QIN AND R. BERRY, Distributed power allocation and scheduling for parallel channel wireless networks, in Proceedings of the Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, 2005, WIOPT, 2005, pp. 77-85.
23. S. SHAKKOTTAI AND R. SRIKANT, Network optimization and control, Found. Trends Network., 2 (2007), pp. 271-379. (Pubitemid 351256642)
24. M. V. SOLODOV AND P. TSENG, Modified projection-type methods for monotone variational inequalities, SIAM J. Control Optim., 34 (1996), pp. 1814-1830. (Pubitemid 126572937)
25. R. SRIKANT, Mathematics of Internet Congestion Control, Birkhäuser Boston, Cambridge, MA, 2004.
26. P. TSENG, On accelerated proximal gradient methods for convex-concave optimization, SIAM J. Optim., submitted.
27. J. TSITSIKLIS, Problems in Decentralized Decision Making and Computation, Ph.D. thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Boston, 1984.
28. H. UZAWA, Iterative methods in concave programming, in Studies in Linear and Nonlinear Programming, Stanford University Press, Standford, 1958, pp. 154-165.
29. H. YIN, U. SHANBHAG, AND P. MEHTA, Nash equilibrium problems with congestion costs and shared constraints, IEEE Trans. Autom. Control, 2009, pp. 4649-4654.
30. H. YIN, U. V. SHANBHAG, AND P. G. MEHTA, Nash equilibrium problems with congestion costs and shared constraints, in IEEE Trans. Automat. Control, 56 (2011), pp. 1702-1708.