Further relaxations of the semidefinite programming approach to sensor network localization

SIAM Journal on Optimization

Volumn 19, Issue 2, 2008, Pages 655-673

  Wang, Zizhuo ^a   Zheng, Song ^b   Ye, Yinyu ^a   Boyd, Stephen ^a  

^a Stanford University   (United States)

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

Author keywords

Chordal graph; Principal submatrix; Second order cone programming; Semidefinite programming; Sensor network localization

Indexed keywords

CHORDAL GRAPH; PRINCIPAL SUBMATRIX; SECOND-ORDER CONE PROGRAMMING; SEMIDEFINITE PROGRAMMING; SENSOR NETWORK LOCALIZATION;

SENSOR NETWORKS;

EID: 60549085200     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/060669395     Document Type: Article

References (37)

1. A. Y. ALFAKIH, Graph rigidity via Euclidean distance matrices, Linear Algebra Appl., 310 (2000), pp. 149-165.
2. A. M.-C So AND Y. YE, Theory of semidefinite programming for sensor network localization, Math. Program., 109 (2007), pp. 367-384.
3. A. Y. ALFAKIH, A. KHANDANI, AND H. WOLKOWICZ, Solving Euclidean distance matrix completion problems via semidefinite programming, Comput. Optim. Appl., 12 (1999), pp. 13-30.
4. A. Y. ALFAKIH, On rigidity and realizability of weighted graphs, Linear Algebra Appl., 325 (2001), pp. 57-70.
5. M. BÂDOIU, Approximation algorithm for embedding metrics into a two-dimensional space, in SODA '03: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2003, pp. 434-443.
6. A. I. BARVINOKDOI, Problems of distance geometry and convex properties of quadratic maps, Discrete Comput. Geom., 13 (1995), pp. 189-202.
7. P. BISWAS AND Y. YE, Semί definite programming for ad hoc wireless sensor network localization, in IPSN 2004 Proceedings of the Third International Symposium on Information Processing in Sensor Networks, ACM, New York, 2004, pp. 46-54.
8. J. BLAIR AND B. PEYTON, An introduction to chordal graphs and clique trees, Inst. Math. Appl., 56 (1993), pp. 1-30.
9. B. GRONE, C. R. JOHNSON, E. M. SA, AND H. WOLKOWICZ, Positive definite completions of partial Hermitian matrices, Linear Algebra Appl., 58 (1984), pp. 109-124.
10. D. GOLDFARB AND K. SCHEINBERG, Interior point trajectories in sernidefinite programming, SIAM J. Optim., 8 (1998), pp. 871-886.
11. O. GÜLER AND Y. YE, Convergence behavior of interior-point algorithms, Math. Program., 60 (1993), pp. 215-228.
12. B. HENDRICKSON, The molecule problem: Exploiting structure in global optimization, SIAM J. Optim., 5 (1995), pp. 835-857.
13. L. HOGBEN, Graph theoretic methods for matrix completion problems, Linear Algebra Appl., 328 (2001), pp. 161-202.
14. C. R. JOHNSON AND R. L. SMITH, The positive definite completion problem relative to a sub-space, Linear Algebra Appl., 307 (2000), pp. 1-14(14).
15. J. ASPNES, D. GOLDENBERG, AND Y. R. YANG, On the computational complexity of sensor network localization, in Algorithmic Aspects of Wireless Sensor Networks: First International Workshop, ALGOSENSORS 2004, Turku, Finland, July 16, 2004. Proceedings, Lecture Notes in Comput. Sci. 3121, Springer-Verlag, New York, 2004, pp. 32-44.
16. J. A. COSTA, N. PATWARI, AND A. O. HERO, III, Distributed weighted-multidimensional scaling for node localization in sensor networks, ACM Trans. Sen. Netw., 2 (2006), pp. 39-64.
17. J. DAHL, V. ROYCHOWDHURY, AND L. VANDENBERGHE, Maximum-Likelihood Estimation of Multivariate Normal, Graphical Models: Large-Scale Numerical Implementation and Topology, Working Paper, Electrical Engineering Department, UCLA, 2006.
18. M. KOJIMA, S. KIM, AND H. WAKI, Sparsity in sums of squares of polynomials, Math. Program., 103 (2005), pp. 45-62.
19. K. Q. WEINBERGER, F. SHA, AND L. K. SAUL, Learning a kernel matrix for nonlinear dimensionality reduction, in ICML '04: Proceedings of the Twenty-First International Conference on Machine Learning, ACM, New York, 2004, p. 106.
20. M. LAURENT, Matrix completion problems, Encyclopedia Optim., 3 (2001), pp. 221-229.
21. L. DOHERTY, K. S. J. PISTER, AND L. EL GHAOUI, Convex position estimation in wireless sensor networks, in INFOCOM 2001 Proceedings of the Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, 2001, pp. 1655-1663.
22. J. J. MORÉ AND Z. WU, Global continuation for distance geometry problems, SIAM J. Optim., 7 (1997), pp. 814-836.
23. M. BÂDOIU, E. D. DEMAINE, M. T. HAJIAGHAYI, AND P. INDYK, Low-dimensional embedding with extra information, Discrete Comput. Geom., 36 (2006), pp. 609-632.
24. M. FUKUDA, M. KOJIMA, K. MUROTA, AND K. NAKATA, Exploiting sparsity in sernidefinite programming via matrix completion I: General framework, SIAM J. Optim., 11 (2000), pp. 647-674.
25. M. W. CARTER, H. H. JIN, M. A. SAUNDERS, AND Y. YE, SpaseLoc: An adaptive subproblem algorithm for scalable wireless sensor network localization, SIAM J. Optim., 17 (2006), pp. 1102-1128.
26. J. NIE, Sum of squares method for sensor network localization, Comput. Optim. Appl., to appear.
27. G. PATAKI, On the rank of extreme matrices in sernidefinite programs and the multiplicity of optimal eignevalues, Math. Oper. Res., 23 (1998), pp. 339-358.
28. P. BISWAS, T.-C. LIANG, K.-C. TOH, Y. YE, AND T.-C WANG, Sernidefinite programming approaches for sensor network localization with noisy distance measurements, IEEE Trans. Automat. Sci. Eng., 3 (2006), pp. 360-371.
29. P. BISWAS, T.-C. LIAN, T.-C. WANG, AND Y. YE, Sernidefinite programming based algorithms for sensor network localization, ACM Trans. Sen. Netw., 2 (2006), pp. 188-220.
30. P. TSENG, Second-order cone programming relaxation of sensor network localization, SIAM J. Optim., 18 (2007), pp. 156-185.
31. A. M.-C. So AND Y. YE, A sernidefinite programming approach to tensegrity theory and re-alizability of graphs, in SODA '06: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, ACM, New York, 2006, pp. 766-775.
32. J. F. STURM, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optim. Methods Softw., 11-12 (1999), pp. 625-653.
33. S. BOYD, P. DlACONIS, AND L. XIAO, Fastest mixing Markov chain on a graph, SIAM Rev., 46 (2004), pp. 667-689.
34. S. J. BENSON, Y. YE, AND X. ZHANG, Solving large-scale sparse semidefinite programs for combinatorial optimization, SIAM J. Optim., 10 (1999), pp. 443-461.
35. T. EREN, O. K. GOLDENBERG, W. WHITELEY, Y. R. YANG, A. S. MORSE, B. D. O. ANDERSON, AND P. N. BELHUMEUR, Rigidity, computation, and randomization in network localization, in INFOCOM 2004 Proceedings of the Twenty-Third Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 4, 2004, pp. 2673-2684.
36. Y. DING, N. KRISLOCK, J. QIAN, AND H. WOLKOWICZ, Sensor Network Localization, Euclidean Distance Matrix. Completions, and Graph Realization, Research report CORR 2006-23, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
37. http://www.stanford.edu/̃yyye/