Algorithm 920: SFSDP: A Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems SFSDP is a Matlab package for solving sensor network localization (SNL) problems. These types of problems arise in monitoring and controlling applications using wireless sensor networks. SFSDP implements the semidefinite programming (SDP) relaxation proposed in Kim et al. [2009] for sensor network localization problems, as a sparse version of the full semidefinite programming relaxation (FSDP) by Biswas and Ye [2004]. To improve the efficiency of FSDP, SFSDP exploits the aggregated and correlative sparsity of a sensor network localization problem. As a result, SFSDP can handle much larger problems than other software as well as three-dimensional anchor-free problems. SFSDP analyzes the input data of a sensor network localization problem, solves the problem, and displays the computed locations of sensors. SFSDP also includes the features of generating test problems for numerical experiments

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  1. Jeyakumar, V.; Kim, S.; Lee, G.M.; Li, G.: Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets (2016)
  2. Jeyakumar, V.; Lasserre, J.B.; Li, G.; Phạm, T.S.: Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems (2016)
  3. Qi, Hou-Duo; Yuan, Xiaoming: Computing the nearest Euclidean distance matrix with low embedding dimensions (2014)
  4. Wu, Changzhi; Li, Chaojie; Long, Qiang: A DC programming approach for sensor network localization with uncertainties in anchor positions (2014)
  5. Zhou, Xiaojun; Gao, David Yang; Yang, Chunhua: Canonical primal-dual algorithm for solving fourth-order polynomial minimization problems (2014)
  6. Bezdek, Károly; Deza, Antoine; Ye, Yinyu: Selected open problems in discrete geometry and optimization (2013)
  7. Kim, Sunyoung; Kojima, Masakazu: A continuation method for large-sized sensor network localization problems (2013)
  8. Kojima, Masakazu; Yamashita, Makoto: Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization (2013)
  9. Malick, Jér^ome; Roupin, Frédéric: On the bridge between combinatorial optimization and nonlinear optimization: a family of semidefinite bounds for 0--1 quadratic problems leading to quasi-Newton methods (2013)
  10. Gouveia, João; Pong, Ting Kei: Comparing SOS and SDP relaxations of sensor network localization (2012)
  11. Kim, Sunyoung; Kojima, Masakazu: Exploiting sparsity in SDP relaxation of polynomial optimization problems (2012)
  12. Kim, Sunyoung; Kojima, Masakazu; Waki, Hayato; Yamashita, Makato: Algorithm 920: SFSDP: a sparse version of full semidefinite programming relaxation for sensor network localization problems (2012)
  13. Krislock, Nathan; Wolkowicz, Henry: Euclidean distance matrices and applications (2012)
  14. Lakhbab, Halima; El Bernoussi, Souad: A hybrid method based on particle swarm optimization and nonmonotone spectral gradient method for unconstrained optimization problem (2012)
  15. Nie, Jiawang; Wang, Li: Regularization methods for SDP relaxations in large-scale polynomial optimization (2012)
  16. Pong, Ting Kei: Edge-based semidefinite programming relaxation of sensor network localization with lower bound constraints (2012)
  17. Yamashita, Makoto; Fujisawa, Katsuki; Fukuda, Mituhiro; Nakata, Kazuhide; Nakata, Maho: Algorithm 925, parallel solver for semidefinite programming problem having sparse Schur complement matrix (2012)
  18. Zheng, Zhenzhen; Luo, Xinlong; Wu, Zhijun: Geometric buildup algorithms for sensor network localization (2012)
  19. Alfakih, Abdo Y.; Anjos, Miguel F.; Piccialli, Veronica; Wolkowicz, Henry: Euclidean distance matrices, semidefinite programming and sensor network localization (2011)
  20. Kim, Sunyoung; Kojima, Masakazu; Mevissen, Martin; Yamashita, Makoto: Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion (2011)

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