SDPpack is our package of Matlab files designed to solve semidefinite programs, which are generalizations of linear programs to the space of block diagonal, symmetric, positive semidefinite matrices. Applications arise in many areas, especially robust control problems in electrical engineering, and in computing provably good approximations to NP-hard graph problems in polynomial time. Semidefinite programs are best solved by interior-point methods, the class of methods introduced by Karmarkar in 1984 to solve linear programs. In 1997, when our software package SDPpack was announced, it implemented a state-of-the-art interior-point method to solve semidefinite programs efficiently and accurately, and it was the first to cover quadratic cone programs as well as semidefinite programs.

References in zbMATH (referenced in 51 articles , 1 standard article )

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  1. Yang, Li; Yu, Bo; Li, YanXi: A homotopy method based on penalty function for nonlinear semidefinite programming (2015)
  2. Yang, Li; Yu, Bo: A homotopy method for nonlinear semidefinite programming (2013)
  3. Gondzio, Jacek: Interior point methods 25 years later (2012)
  4. Ling, Ai-fan; Xu, Cheng-xian: A new discrete filled function method for solving large scale max-cut problems (2012)
  5. Xu, Fengmin; Ma, Xusheng; Chen, Baili: A new Lagrangian net algorithm for solving max-bisection problems (2011)
  6. Colombo, Marco; Gondzio, Jacek: Further development of multiple centrality correctors for interior point methods (2008)
  7. Ling, Ai-Fan; Xu, Cheng-Xian; Tang, Le: A modified VNS metaheuristic for max-bisection problems (2008)
  8. Brimkov, Valentin: Algorithmic and explicit determination of the Lovász number for certain circulant graphs (2007)
  9. Hachicho, O.: A novel LMI-based optimization algorithm for the guaranteed estimation of the domain of attraction using rational Lyapunov functions (2007)
  10. Lobo, Miguel Sousa; Fazel, Maryam; Boyd, Stephen: Portfolio optimization with linear and fixed transaction costs (2007)
  11. Mu, Xuewen; Zhang, Yaling; Liu, Sanyang: A successive quadratic programming algorithm for SDP relaxation of Max-Bisection (2007)
  12. Xu, Feng Min; Xu, Cheng Xian; Li, Xing Si: A continuation algorithm for max-cut problem (2007)
  13. Al-Homidan, S.: Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem (2006)
  14. Xu, Cheng-xian; He, Xiao-liang; Xu, Feng-min: An effective continuous algorithm for approximate solutions of large scale max-cut problems (2006)
  15. Meurdesoif, Philippe: Strengthening the Lovász $\theta(\overline G)$ bound for graph coloring (2005)
  16. Vandenberghe, Lieven; Balakrishnan, V. Ragu; Wallin, Ragnar; Hansson, Anders; Roh, Tae: Interior-point algorithms for semidefinite programming problems derived from the KYP lemma (2005)
  17. Brimkov, Valentin E.: Clique, chromatic, and Lovász numbers of certain circulant graphs (2004)
  18. Liu, Hongwei; Liu, Sanyang; Xu, Fengmin: A tight semidefinite relaxation of the MAX CUT problem (2003)
  19. Pinar, Mustapha Ç.: A derivation of Lovász’ theta via augmented Lagrange duality (2003)
  20. Sparks, Rebecca: On bounds for the existence of a bistable controller. (2003)

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