SDPHA: A MATLAB implementation of homogeneous interior-point algorithms for semidefinite programming. Mehrotra type primal-dual predictor-corrector interior-point algorithms for semidefinite programming are implemented, using the homogeneous formulation proposed and analyzed by Potra and Sheng. Several search directions, including the AHO, HKM, NT, Toh, and Gu directions, are used. A rank-2 update technique is employed in our MATLAB code so that the computation of homogeneous directions is only slightly more expensive than in the non-homogeneous case. However, the homogeneous algorithms generally take fewer iterations to compute an approximate solution within a desired accuracy. Numerical results show that the homogeneous algorithms outperform their non-homogeneous counterparts, with improvement of more than 20% in many cases, in terms of total CPU time.

References in zbMATH (referenced in 35 articles , 1 standard article )

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  1. Permenter, Frank; Friberg, Henrik A.; Andersen, Erling D.: Solving conic optimization problems via self-dual embedding and facial reduction: A unified approach (2017)
  2. Nayak, Rupaj Kumar; Desai, Jitamitra: A modified homogeneous potential reduction algorithm for solving the monotone semidefinite linear complementarity problem (2016)
  3. Wang, G.Q.; Bai, Y.Q.; Gao, X.Y.; Wang, D.Z.: Improved complexity analysis of full Nesterov-Todd step interior-point methods for semidefinite optimization (2015)
  4. Jin, S.; Ariyawansa, K.A.; Zhu, Y.: Homogeneous self-dual algorithms for stochastic semidefinite programming (2012)
  5. Al-Homidan, Suliman; Alshahrani, Mohammad M.; Petra, Cosmin G.; Potra, Florian A.: Minimal condition number for positive definite Hankel matrices using semidefinite programming (2010)
  6. Pólik, Imre; Terlaky, Tamás: Interior point methods for nonlinear optimization (2010)
  7. Teixeira, A.; Bastos, F.: On using quadratic interpolation of the determinant function to estimate the step-length in a predictor-corrector variant for semidefinite programming (2009)
  8. Nemirovski, Arkadi: Advances in convex optimization: conic programming (2007)
  9. Shen, Yijiang; Lam, Edmund Y.; Wong, Ngai: Robust binary image deconvolution with positive semidefinite programming (2007)
  10. Freund, Robert M.: On the behavior of the homogeneous self-dual model for conic convex optimization (2006)
  11. Kuo, Yu-Ju; Mittelmann, Hans D.: Interior point methods for second-order cone programming and OR applications (2004)
  12. Zhang, Shuzhong: A new self-dual embedding method for convex programming (2004)
  13. De Klerk, Etienne: Aspects of semidefinite programming. Interior point algorithms and selected applications (2002)
  14. Henrion, Didier; Sagimoto, Kenji; Šebek, Michael: Rank-one LMI approach to robust stability of polynomial matrices. (2002)
  15. Peng, Jiming; Roos, Cornelis; Terlaky, Tamás: Self-regularity: a new paradigm for primal-dual interior-point algorithms (2002)
  16. Toh, Kim-Chuan: A note on the calculation of step-lengths in interior-point methods for semidefinite programming (2002)
  17. Zhang, Shao-Liang; Nakata, Kazuhide; Kojima, Masakazu: Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming (2002)
  18. Henrion, Didier; Šebek, Michael; Bachelier, Olivier: Rank-one LMI approach to stability of 2-D polynomial matrices (2001)
  19. Kruk, Serge; Muramatsu, Masakazu; Rendl, Franz; Vanderbei, Robert J.; Wolkowicz, Henry: The Gauss-Newton direction in semidefinite programming (2001)
  20. Mizuno, Shinji; Todd, Michael J.: On two homogeneous self-dual approaches to linear programming and its extensions. (2001)

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