Convex optimization, game theory, and variational inequality theory

IEEE Signal Processing Magazine

Volumn 27, Issue 3, 2010, Pages 35-49

  Scutari, Gesualdo ^a,b   Palomar, Daniel ^c   Facchinei, Francisco ^b   Pang, Jong Shi ^d  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^c HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

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

Author keywords

[No Author keywords available]

Indexed keywords

COGNITIVE RADIO; COGNITIVE SYSTEMS; CONGESTION CONTROL (COMMUNICATION); CONVEX OPTIMIZATION; COOPERATIVE COMMUNICATION; NONLINEAR ANALYSIS; PEER TO PEER NETWORKS; POWER CONTROL; RADIO SYSTEMS; SIGNAL PROCESSING; VARIATIONAL TECHNIQUES;

APPLIED MATHEMATICS; CLASSICAL GAME THEORY; COMMUNICATIONS AND NETWORKINGS; CONVEX OPTIMIZATION TECHNIQUES; MULTIUSER COMMUNICATION SYSTEMS; OPTIMIZATION PROBLEMS; SIGNAL PROCESSING ALGORITHMS; VARIATIONAL INEQUALITIES;

GAME THEORY;

EID: 85032758255     PISSN: 10535888     EISSN: None     Source Type: Journal    
DOI: 10.1109/MSP.2010.936021     Document Type: Article

References (37)

1. M. Chiang, S. H. Low, Z.-Q. Luo, N. B. Shroff, W. Yu, IEEE J. Select. Areas Commun. (Special Issue on Nonlinear Optimization for Communication Systems) vol. 24, 8, Aug. 2006. 93.
2. Y. Eldar, T. Davidson, A. B. Gershman, and Z.-Q. Luo, IEEE J. Select. Topics Signal Processing (Special Issue on Convex Optimization Methods for Signal Processing), vol.1, no.4, Dec. 2007.
3. M. J. Osborne and A. Rubinstein, A Course in Game Theory. Cambridge, MA: MIT Press, July 2004.
4. J.-P. Aubin, Mathematical Method for Game and Economic Theory. New York: Dover, Nov. 2007.
5. W. Yu, G. Ginis, and J. M. Cioffi, "Distributed multiuser power control for digital subscriber lines," IEEE J. Select. Areas Commun., vol.20, no.5, pp. 1105-1115, June 2002.
6. Z.-Q. Luo and J.-S. Pang, "Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines," EURASIP J. Appl. Signal Processing, vol.2006, pp. 1-10, May 2006.
7. R. Cendrillon, J. Huang, M. Chiang, and M. Moonen, "Autonomous spectrum balancing for digital subscriber lines," IEEE Trans. Signal Processing, vol.55, no.8, pp. 4241-4257, Aug. 2007.
8. G. Scutari, D. P. Palomar, and S. Barbarossa, "Optimal linear precoding strategies for wideband noncooperative systems based on game theory\Parts I/& II: Nash equilibria/& Algorithms," IEEE Trans. Signal Processing, vol.56, no.3, pp. 1230-1249/& 1250-1267, Mar. 2008. (Pubitemid 351386281)
9. G. Scutari, D. P. Palomar, and S. Barbarossa, "Asynchronous iterative water-filling for Gaussian frequency-selective interference channels," IEEE Trans. Inform. Theory, vol.54, no.7, pp. 2868-2878, July 2008.
10. J.-S. Pang, G. Scutari, F. Facchinei, and C. Wang, "Distributed power allocation with rate constraints in Gaussian parallel interference channels," IEEE Trans. Inform. Theory, vol.54, no.8, pp. 3471-3489, Aug. 2008.
11. G. Scutari, D. P. Palomar, and S. Barbarossa, "Competitive design of multiuser MIMO systems based on game theory: A unified view," IEEE J. Select. Areas Com-mun., vol.26, no.7, pp. 1089-1103, Sept. 2008.
12. G. Scutari, D. P. Palomar, and S. Barbarossa, "The MIMO iterative waterfill-ing algorithm," IEEE Trans. Signal Processing, vol.57, no.5, pp. 1917-1935, May 2009.
13. Z. Ji and K. R. Liu, "Dynamic spectrum sharing: A game theoretical overview," IEEE Commun. Mag., vol.45, no.5, pp. 88-94, May 2007.
14. G. Scutari, D. P. Palomar, and S. Barbarossa, "Cognitive MIMO radio: Competitive optimality design based on subspace projections," IEEE Signal Processing Mag., vol.25, no.6, pp. 46-59, Nov. 2008.
15. G. Scutari and D. P. Palomar, "MIMO cognitive radio: A game theoretical approach," IEEE Trans. Signal Processing, vol.58, no.2, pp. 761-780, Feb. 2010.
16. G. Scutari, D. P. Palomar, and S. Barbarossa, "Competitive optimization of cognitive radio MIMO systems via game theory," in Convex Optimization in Signal Processing and Communications, D. P. Palomar and Y. C. Eldar, Eds. London: Cambridge Univ. Press, 2009, ch. 11, pp. 387-442.
17. J.-S. Pang, G. Scutari, D. P. Palomar, and F. Facchinei, "Design of cognitive radio systems under temperature-interference constraints: A variational inequality approach," IEEE Trans. Signal Processing, to be published.
18. E. Altman, T. Boulogne, R. E. Azouzi, T. Jimenez, and L. Wynter, "A survey on networking games," Comput. Oper. Res., vol.33, no.2, pp. 286-311, 2006.
19. T. Alpcan and T. Basar, "A game-theoretic framework for congestion control in general topology networks," in Proc. 41st IEEE Conf. Decision and Control (CDC 2002), Las Vegas, NV, Dec. 10-13, 2002, vol.2, pp. 1218-1224.
20. J. Huang, D. P. Palomar, N. Ma ndaya m, J. Walrand, S. B. Wicker, and T. Basar, IEEE J. Select. Areas Commun. (Special Issue on Game Theory in Communication Systems), vol.26, no.7, Sept. 2008.
21. E. A. Jorswieck, E. G. Larsson, M. Luise, and H. V. Poor, "Game theory and the flat-fading gaussian interference channel," IEEE Signal Processing Mag.(Special Issue on Game Theory in Signal Processing and Communications), vol.26, no.5, pp. 18-27, Sept. 2009.
22. F. Facchinei and J.-S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problem. New York: Springer, 2003.
23. F. Facchinei and C. Kanzow, "Generalized Nash equilibrium problems," Quart. J. Oper. Res.(4 OR), vol.5, no.3, pp. 173-210, Sept. 2007.
24. D. P. Bertsekas, A. Nedich, and A. Ozdaglar, Convex Analysis and Optimization. Belmont, MA: Athena Scientific, 2003.
25. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2003.
26. R. W. Cottle, "Nonlinear programs with positively bounded Jacobians," SIAM J. Appl. Math., vol.14, no.1, pp. 147-158, 1966.
27. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation: Numerical Methods, 2nd ed. Belmont, MA: Athena Scientific, 1989.
28. F. Facchinei and J.-S. Pang, "Nash equilibria: The variational approach," in Convex Optimization in Signal Processing and Communications, D. P. Palomar and Y. C. Eldar, Eds. London: Cambridge Univ. Press, 2009, ch. 12, pp. 443-493.
29. D. Monderer and L. S. Shapley, "Potential games," Games Econ. Behav., vol.14, no.1, pp. 124-143, May 1996.
30. D. Topkis, Supermodularity and Complementarity. Princeton, NJ: Princeton Univ. Press, 1998.
31. E. Altman and Z. Altman, "S\modular games and power control in wireless networks," IEEE Trans. Automat. Contr., vol.48, no.5, pp. 839-842, May 2003.
32. J. Huang, R. Berry, and M. L. Honig, "Distributed interference compensation for wireless networks," IEEE J. Select. Areas Commun., vol.24, no.5, pp. 1074-1084, May 2006.
33. G. Scutari, D. P. Palomar, J.-S. Pang, and F. Facchinei, "Flexible design of cognitive radio wireless systems: From game theory to variational inequality theory," IEEE Signal Processing Mag., vol.26, no.5, pp. 107-123, Sept. 2009.
34. F. Facchinei, A. Fischer, and V. Piccialli, "On generalized nash games and variational inequalities," Oper. Res. Lett., vol.35, no.2, pp. 159-164, 2007.
35. G. Scutari, "Competition and cooperation in wireless communication networks," Ph.D. dissertation, INFOCOM Dept., Univ. Rome, La Sapienza, Nov. 2004.
36. S. Haykin, "Cognitive radio: Brain-empowered wireless communications," IEEE J. Select. Areas Commun., vol.23, no.2, pp. 201-220, Feb. 2005.
37. F. Facchinei, V. Piccialli, and M. Sciandrone, "Decomposition algorithms for generalized potential games," submitted for publication.