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Semidefinite programming based approaches for realtime tractor localization in port container terminals
1.  Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China, China 
2.  Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 
References:
[1] 
A. Y. Alfakih, A. Khandani and H. Wolkowicz, Solving Euclidean distance matrix completion problems via semidefinite programming,, Computational optimization and applications, 12 (1999), 13. doi: 10.1023/A:1008655427845. 
[2] 
X. Bai, X. Zheng and X. Sun, A survey on probabilistically constrainted optimization problems,, Numerical Algebra, 2 (2012), 767. doi: 10.3934/naco.2012.2.767. 
[3] 
P. Biswas, T.C. Liang, K.C. Toh, Y. Ye and T.C. Wang, Semidefinite programming approaches for sensor network localization with noisy distance measurements,, IEEE transactions on automation science and engineering, 3 (2006), 360. 
[4] 
P. Biswas, T. C. Liang, T. C. Wang and Y. Ye, Semidefinite programming based algorithms for sensor network localization,, ACM Transactions on Sensor Networks, 2 (2006), 188. 
[5] 
P. Biswas, K. C. Toh and Y. Ye, A distributed SDP approach for largescale noisy anchorfree graph realization with applications to molecular conformation,, SIAM Journal on Scientific Computing, 30 (2007), 1251. doi: 10.1137/05062754X. 
[6] 
P. Biswas and Y. Ye, Semidefinite programming for ad hoc wireless sensor network localization,, in, (2004), 46. 
[7] 
J.A. Costa, N. Patwari, and A.O. Hero, III, Distributed weightedmultidimensional scaling for node localization in sensor networks,, ACM Transactions on Sensor Networks, 2 (2006), 39. 
[8] 
L. Doherty, K. S. J. Pister and L. El Ghaoui, Convex position estimation in wireless sensor networks,, in, (2001), 1655. 
[9] 
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, (2004), 2673. 
[10] 
D. Ganesan, B. Krishnamachari, A. Woo, D. Culler, D. Estrin and S. Wicker, "An Empirical Study of Epidemic Algorithms in Large Scale Multihop Wireless Networks,", Intel Corporation, (2002). 
[11] 
M. Gerdts, R. Henrion, D. Homberg and C. Landry, Path planning and collision avoidance for robots,, Numerical Algebra, 2 (2012), 437. doi: 10.3934/naco.2012.2.437. 
[12] 
A. A. Kannan, G. Mao and B. Vucetic, Simulated annealing based localization in wireless sensor network,, in, (2005), 513. 
[13] 
S. Kim, M. Kojima and H. Waki, Exploiting sparsity in SDP relaxation for sensor network localization,, SIAM Journal on Optimization, 20 (2009), 192. doi: 10.1137/080713380. 
[14] 
J. Lofberg, YALMIP: A toolbox for modeling and optimization in MATLAB,, in Proc. Int. Symp. CACSD, (2004), 284. 
[15] 
K. W. K. Lui, W. K. Ma, H. C. So and F. K. W. Chan, Semidefinite programming algorithms for sensor network node localization with uncertainties in anchor positions and/or propagation speed,, IEEE Transactions on Signal Processing, 57 (2009), 752. doi: 10.1109/TSP.2008.2007916. 
[16] 
J. J. Mor and Z. Wu, Global continuation for distance geometry problems,, SIAM Journal on Optimization, 7 (1997), 814. doi: 10.1137/S1052623495283024. 
[17] 
E. NiewiadomskaSzynkiewicz and M. Marks, Optimization schemes for wireless sensor network localization,, International Journal of Applied Mathematics and Computer Science, 19 (2009), 291. 
[18] 
R. W. Ouyang, A. K. Wong and C. T. Lea, Received signal strengthbased wireless localization via semidefinite programming: noncooperative and cooperative schemes,, IEEE Transactions on Vehicular Technology, 59 (2010), 1307. 
[19] 
A. M. C. So and Y. Ye, Theory of semidefinite programming for sensor network localization,, Mathematical Programming, 109 (2007), 367. doi: 10.1007/s1010700600401. 
[20] 
D. Steenken, S. Vos and R. Stahlbock, Container terminal operation and operations research  a classification and literature review,, OR Spectrum, 26 (2004), 3. doi: 10.1007/s0029100701009. 
[21] 
J. F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,, Optimization Methods and Software, 11 (1999), 625. doi: 10.1080/10556789908805766. 
[22] 
J. Sun, On methods for solving nonlinear semidefinite optimization problems,, Numerical Algebra, 1 (2011), 1. doi: 10.3934/naco.2011.1.1. 
[23] 
K. C. Toh, M. J. Todd and R. H. Tutuncu, SDPT3  a Matlab software package for semidefinite programming,, Optimization Methods and Software, 11 (1999), 545. doi: 10.1080/10556789908805762. 
[24] 
P. Tseng, Secondorder cone programming relaxation of sensor network localization,, SIAM Journal on Optimization, 18 (2008), 156. doi: 10.1137/050640308. 
[25] 
H. Waki, S. Kim, M. Kojima and M. Muramatsu, Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity,, SIAM Journal on Optimization, 17 (2006), 218. doi: 10.1137/050623802. 
[26] 
S. Y. Wang and Y. W. Li, Evaluation of intelligent traffic signal control algorithms under realistic landmarkbased traffic pattern over the NCTUns network simulator,, in, (2012), 379. 
[27] 
Z. Wang, S. Zheng, S. Boyd and Y. Ye, Further relaxations of the SDP approach to sensor network localization,, SIAM Journal on Optimization, 19 (2008), 655. doi: 10.1137/060669395. 
[28] 
S. Zhang, J. Cao, L. Chen and D. Chen, Accurate and energyefficient rangefree localization for mobile sensor networks,, IEEE Transactions on Mobile Computing, 9 (2010), 897. 
show all references
References:
[1] 
A. Y. Alfakih, A. Khandani and H. Wolkowicz, Solving Euclidean distance matrix completion problems via semidefinite programming,, Computational optimization and applications, 12 (1999), 13. doi: 10.1023/A:1008655427845. 
[2] 
X. Bai, X. Zheng and X. Sun, A survey on probabilistically constrainted optimization problems,, Numerical Algebra, 2 (2012), 767. doi: 10.3934/naco.2012.2.767. 
[3] 
P. Biswas, T.C. Liang, K.C. Toh, Y. Ye and T.C. Wang, Semidefinite programming approaches for sensor network localization with noisy distance measurements,, IEEE transactions on automation science and engineering, 3 (2006), 360. 
[4] 
P. Biswas, T. C. Liang, T. C. Wang and Y. Ye, Semidefinite programming based algorithms for sensor network localization,, ACM Transactions on Sensor Networks, 2 (2006), 188. 
[5] 
P. Biswas, K. C. Toh and Y. Ye, A distributed SDP approach for largescale noisy anchorfree graph realization with applications to molecular conformation,, SIAM Journal on Scientific Computing, 30 (2007), 1251. doi: 10.1137/05062754X. 
[6] 
P. Biswas and Y. Ye, Semidefinite programming for ad hoc wireless sensor network localization,, in, (2004), 46. 
[7] 
J.A. Costa, N. Patwari, and A.O. Hero, III, Distributed weightedmultidimensional scaling for node localization in sensor networks,, ACM Transactions on Sensor Networks, 2 (2006), 39. 
[8] 
L. Doherty, K. S. J. Pister and L. El Ghaoui, Convex position estimation in wireless sensor networks,, in, (2001), 1655. 
[9] 
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, (2004), 2673. 
[10] 
D. Ganesan, B. Krishnamachari, A. Woo, D. Culler, D. Estrin and S. Wicker, "An Empirical Study of Epidemic Algorithms in Large Scale Multihop Wireless Networks,", Intel Corporation, (2002). 
[11] 
M. Gerdts, R. Henrion, D. Homberg and C. Landry, Path planning and collision avoidance for robots,, Numerical Algebra, 2 (2012), 437. doi: 10.3934/naco.2012.2.437. 
[12] 
A. A. Kannan, G. Mao and B. Vucetic, Simulated annealing based localization in wireless sensor network,, in, (2005), 513. 
[13] 
S. Kim, M. Kojima and H. Waki, Exploiting sparsity in SDP relaxation for sensor network localization,, SIAM Journal on Optimization, 20 (2009), 192. doi: 10.1137/080713380. 
[14] 
J. Lofberg, YALMIP: A toolbox for modeling and optimization in MATLAB,, in Proc. Int. Symp. CACSD, (2004), 284. 
[15] 
K. W. K. Lui, W. K. Ma, H. C. So and F. K. W. Chan, Semidefinite programming algorithms for sensor network node localization with uncertainties in anchor positions and/or propagation speed,, IEEE Transactions on Signal Processing, 57 (2009), 752. doi: 10.1109/TSP.2008.2007916. 
[16] 
J. J. Mor and Z. Wu, Global continuation for distance geometry problems,, SIAM Journal on Optimization, 7 (1997), 814. doi: 10.1137/S1052623495283024. 
[17] 
E. NiewiadomskaSzynkiewicz and M. Marks, Optimization schemes for wireless sensor network localization,, International Journal of Applied Mathematics and Computer Science, 19 (2009), 291. 
[18] 
R. W. Ouyang, A. K. Wong and C. T. Lea, Received signal strengthbased wireless localization via semidefinite programming: noncooperative and cooperative schemes,, IEEE Transactions on Vehicular Technology, 59 (2010), 1307. 
[19] 
A. M. C. So and Y. Ye, Theory of semidefinite programming for sensor network localization,, Mathematical Programming, 109 (2007), 367. doi: 10.1007/s1010700600401. 
[20] 
D. Steenken, S. Vos and R. Stahlbock, Container terminal operation and operations research  a classification and literature review,, OR Spectrum, 26 (2004), 3. doi: 10.1007/s0029100701009. 
[21] 
J. F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,, Optimization Methods and Software, 11 (1999), 625. doi: 10.1080/10556789908805766. 
[22] 
J. Sun, On methods for solving nonlinear semidefinite optimization problems,, Numerical Algebra, 1 (2011), 1. doi: 10.3934/naco.2011.1.1. 
[23] 
K. C. Toh, M. J. Todd and R. H. Tutuncu, SDPT3  a Matlab software package for semidefinite programming,, Optimization Methods and Software, 11 (1999), 545. doi: 10.1080/10556789908805762. 
[24] 
P. Tseng, Secondorder cone programming relaxation of sensor network localization,, SIAM Journal on Optimization, 18 (2008), 156. doi: 10.1137/050640308. 
[25] 
H. Waki, S. Kim, M. Kojima and M. Muramatsu, Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity,, SIAM Journal on Optimization, 17 (2006), 218. doi: 10.1137/050623802. 
[26] 
S. Y. Wang and Y. W. Li, Evaluation of intelligent traffic signal control algorithms under realistic landmarkbased traffic pattern over the NCTUns network simulator,, in, (2012), 379. 
[27] 
Z. Wang, S. Zheng, S. Boyd and Y. Ye, Further relaxations of the SDP approach to sensor network localization,, SIAM Journal on Optimization, 19 (2008), 655. doi: 10.1137/060669395. 
[28] 
S. Zhang, J. Cao, L. Chen and D. Chen, Accurate and energyefficient rangefree localization for mobile sensor networks,, IEEE Transactions on Mobile Computing, 9 (2010), 897. 
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