Nonnegative matrix inequalities and their application to nonconvex power control optimization

SIAM Journal on Matrix Analysis and Applications

Volumn 32, Issue 3, 2011, Pages 1030-1055

  Tan, Chee Wei ^a   Friedland, Shmuel ^b,c   Low, Steven ^d  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^c Berlin Mathematical School   (Germany)

^d CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Convex relaxation; Maximization of convex functions; Nonconvex optimization; Nonnegative matrix theory; Spectral radii of irreducible nonnegative matrices; Wireless networks

Indexed keywords

CONTROL OPTIMIZATION; CONVEX RELAXATION; CONVEX SET; CONVEXIFICATION; ENGINEERING APPLICATIONS; GAUSSIAN CHANNELS; GLOBAL OPTIMIZATION ALGORITHM; LAGRANGE DUAL; MAXIMIZATION PROBLEM; MULTI-USER; NON-NEGATIVE MATRIX; NONCONVEX; NONCONVEX OPTIMIZATION; NP-HARD PROBLEM; OPTIMAL POWER CONTROL; PERRON-FROBENIUS THEOREM; POWER DOMAIN; PROBLEM STRUCTURE; RELAXATION TECHNIQUES; SIGNAL-TO-INTERFERENCE NOISE RATIO; SPECTRAL RADII; SUBOPTIMALITY; SUM-RATE; TIGHT BOUND; WIRELESS COMMUNICATION NETWORK;

CODE DIVISION MULTIPLE ACCESS; COMPUTATIONAL COMPLEXITY; GLOBAL OPTIMIZATION; INVERSE PROBLEMS; OPTIMIZATION; POWER CONTROL; RELAXATION PROCESSES; SET THEORY; TELECOMMUNICATION; THEOREM PROVING; WIRELESS NETWORKS; WIRELESS TELECOMMUNICATION SYSTEMS;

MATRIX ALGEBRA;

EID: 80054026733     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/090757137     Document Type: Article

References (24)

1. V. BALAKRISHNAN, S. BOYD, AND S. BALEMI, Branch and bound algorithm for computing the minimum stability degree of parameter-dependent linear systems, Int. J. Robust Nonlinear Control, 1 (1991), pp. 295-317.
2. A. BERMAN AND R. J. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
3. S. BOYD AND L. VANDENBERGHE, Convex Optimization, Cambridge University Press, Cambridge, 2004.
4. M. CHIANG, P. HANDE, T. LAN, AND C. W. TAN, Power control in wireless cellular networks, Foundations and Trends in Networking, 2 (2008), pp. 381-533.
5. M. CHIANG, C. W. TAN, D. P. PALOMAR, D. O'NEILL, AND D. JULIAN, Power control by geometric programming, IEEE Trans. Wireless Communications, 6 (2007), pp. 2640-2651.
6. T. M. COVER AND J. A. THOMAS, Elements of Information Theory, John Wiley & Sons, New York, 1991.
7. M. EBRAHIMI, M. A. MADDAH-ALI, AND A. K. KHANDANI, Power allocation and asymptotic achievable sum-rates in single-hop wireless networks, in Proceedings of the 40th Annual IEEE Conference on Information Sciences and Systems, 2006.
8. J. E. FALK, Lagrange multipliers and nonconvex programs, SIAM J. Control, 7 (1969), pp. 534-545.
9. G. J. FOSCHINI AND Z. MILJANIC, A simple distributed autonomous power control algorithm and its convergence, IEEE Trans. Vehicular Tech., 42 (1993), pp. 641-646.
10. S. FRIEDLAND AND S. KARLIN, Some inequalities for the spectral radius of non-negative matrices and applications, Duke Math. J., 42 (1975), pp. 459-490.
11. F. R. GANTMACHER, The Theory of Matrices, Vol. II, Chelsea, New York, 1974.
12. M. GRANT AND S. BOYD, CVX: Matlab Software for Disciplined Convex Programming, Version 1.21, http://cvxr.com/cvx (2011).
13. R. HORST AND H. TUY, Global Optimization: Deterministic Approaches, 3rd ed., Springer, New York, 1995.
14. J. F. C. KINGMAN, A convexity property of positive matrices, Q. J. Math, 12 (1961), pp. 283-284.
15. Z.-Q. LUO AND W. YU, An introduction to convex optimization for communications and signal processing (tutorial paper), IEEE J. Selected Areas Commun., 24 (2006), pp. 1426-1438.
16. Z.-Q. LUO AND Z. ZHANG, Dynamic spectrum management: Complexity and duality, IEEE J. Selected Areas Signal Process., 2 (2008), pp. 57-73. (Pubitemid 351392288)
17. Z.-Q. LUO AND Z. ZHANG, Duality gap estimation and polynomial time approximation for optimal spectrum management, IEEE Trans. Signal Process., 57 (2009), pp. 2675-2689.
18. B. R. MARKS AND G. P. WRIGHT, A general inner approximation algorithm for nonconvex mathematical programs, Oper. Res., 26 (1978), pp. 681-683.
19. C. W. TAN, S. FRIEDLAND, AND S. H. LOW, Spectrum management in multiuser cognitive wireless networks: Optimality and algorithms, IEEE J. Selected Areas Commun., 29 (2011), pp. 421-430.
20. C. W. TAN, M. CHIANG, AND R. SRIKANT, Fast algorithms and performance bounds for sum rate maximization in wireless networks, in Proceedings of the IEEE Conference on Computer Communications (Infocom), 2009.
21. C. W. TAN, M. CHIANG, AND R. SRIKANT, Maximizing sum rate and minimizing MSE on multiuser downlink: Optimality, fast algorithm, and equivalence via max-min SIR, in Proceedings of the IEEE International Symposium on Information Theory (ISIT), 2009.
22. C. W. TAN, D. P. PALOMAR, AND M. CHIANG, Solving nonconvex power control problems in wireless networks: Low SIR regime and distributed algorithms, in Proceedings of the IEEE Global Communications (Globecom), 2005.
23. H. TUY, T. V. THIEU, AND N. Q. THAI, A conical algorithm for globally minimizing a concave function over a closed convex set, Math. Oper. Res., 10 (1985), pp. 498-514. (Pubitemid 15562373)
24. W. YU AND R. LUI, Dual methods for nonconvex spectrum optimization of multicarrier systems, IEEE Trans. Commun., 54 (2006), pp. 1310-1322. (Pubitemid 44111460)