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. Cerone, Vito; Razza, Valentino; Regruto, Diego: One-shot set-membership identification of generalized Hammerstein-Wiener systems (2020)
  2. Campos, Juan S.; Misener, Ruth; Parpas, Panos: A multilevel analysis of the Lasserre hierarchy (2019)
  3. Dressler, Mareike; Iliman, Sadik; de Wolff, Timo: An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming (2019)
  4. Ito, Naoki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Toh, Kim-Chuan: Algorithm 996: BBCPOP: a sparse doubly nonnegative relaxation of polynomial optimization problems with binary, box, and complementarity constraints (2019)
  5. Kimizuka, Masaki; Kim, Sunyoung; Yamashita, Makoto: Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods (2019)
  6. Kuang, Xiaolong; Ghaddar, Bissan; Naoum-Sawaya, Joe; Zuluaga, Luis F.: Alternative SDP and SOCP approximations for polynomial optimization (2019)
  7. Kussaba, Hugo T. M.; Ishihara, João Y.; Menezes, Leonardo R. A. X.: A robust unscented transformation for uncertain moments (2019)
  8. Campos, Juan S.; Parpas, Panos: A multigrid approach to SDP relaxations of sparse polynomial optimization problems (2018)
  9. Cerone, Vito; Razza, Valentino; Regruto, Diego: Set-membership errors-in-variables identification of MIMO linear systems (2018)
  10. Zhao, Kang; Cheng, Lizhi; Li, Shengguo; Liao, Anping: A new updating method for the damped mass-spring systems (2018)
  11. Ghaddar, Bissan; Claeys, Mathieu; Mevissen, Martin; Eck, Bradley J.: Polynomial optimization for water networks: global solutions for the valve setting problem (2017)
  12. Kim, Sunyoung; Kojima, Masakazu: Binary quadratic optimization problems that are difficult to solve by conic relaxations (2017)
  13. Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
  14. Dalkiran, Evrim; Sherali, Hanif D.: RLT-POS: reformulation-linearization technique-based optimization software for solving polynomial programming problems (2016)
  15. de Klerk, Etienne: Book review of: J.-B. Lasserre, An introduction to polynomial and semi-algebraic optimization (2016)
  16. 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)
  17. Klep, Igor; Povh, Janez: Constrained trace-optimization of polynomials in freely noncommuting variables (2016)
  18. Lasserre, Jean Bernard: An introduction to polynomial and semi-algebraic optimization (2015)
  19. Wittek, Peter: Algorithm 950: Ncpol2sdpa -- sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables (2015)
  20. Magron, Victor: NLCertify: a tool for formal nonlinear optimization (2014)

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