SparsePOP: a sparse semidefinite programming relaxation of polynomial optimization problems. SparsePOP is a Matlab implementation of the sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki et al. [2006]. The sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying “a hierarchy of LMI relaxations of increasing dimensions” Lasserre [2006]. The efficiency of SparsePOP to approximate optimal solutions of POPs is thus increased, and larger-scale POPs can be handled.

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  1. Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
  2. de Klerk, Etienne: Book review of: J.-B. Lasserre, An introduction to polynomial and semi-algebraic optimization (2016)
  3. 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)
  4. Klep, Igor; Povh, Janez: Constrained trace-optimization of polynomials in freely noncommuting variables (2016)
  5. Lasserre, Jean Bernard: An introduction to polynomial and semi-algebraic optimization (2015)
  6. Magron, Victor: NLCertify: a tool for formal nonlinear optimization (2014)
  7. Allamigeon, Xavier; Gaubert, Stéphane; Magron, Victor; Werner, Benjamin: Certification of bounds of non-linear functions: the templates method (2013)
  8. Burgdorf, Sabine; Cafuta, Kristijan; Klep, Igor; Povh, Janez: The tracial moment problem and trace-optimization of polynomials (2013)
  9. Cerone, V.; Piga, D.; Regruto, D.: Bounding the parameters of block-structured nonlinear feedback systems (2013)
  10. Dalkiran, Evrim; Sherali, Hanif D.: Theoretical filtering of RLT bound-factor constraints for solving polynomial programming problems to global optimality (2013)
  11. Kojima, Masakazu; Yamashita, Makoto: Enclosing ellipsoids and elliptic cylinders of semialgebraic sets and their application to error bounds in polynomial optimization (2013)
  12. Mizutani, Tomohiko; Yamashita, Makoto: Correlative sparsity structures and semidefinite relaxations for concave cost transportation problems with change of variables (2013)
  13. Waki, Hayato; Muramatsu, Masakazu: Facial reduction algorithms for conic optimization problems (2013)
  14. Anjos, Miguel F.; Lasserre, Jean B.: Introduction to semidefinite, conic and polynomial optimization (2012)
  15. Cafuta, Kristijan; Klep, Igor; Povh, Janez: Constrained polynomial optimization problems with noncommuting variables (2012)
  16. Cerone, V.; Piga, D.; Regruto, D.: Bounded error identification of Hammerstein systems through sparse polynomial optimization (2012)
  17. Chen, Bilian; He, Simai; Li, Zhening; Zhang, Shuzhong: Maximum block improvement and polynomial optimization (2012)
  18. Greuet, Aurélien; Guo, Feng; El Din, Mohab Safey; Zhi, Lihong: Global optimization of polynomials restricted to a smooth variety using sums of squares (2012)
  19. Kim, Sunyoung; Kojima, Masakazu: Exploiting sparsity in SDP relaxation of polynomial optimization problems (2012)
  20. Takano, Yuichi; Sotirov, Renata: A polynomial optimization approach to constant rebalanced portfolio selection (2012)

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