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## Superlinear Convergence of Interior-Point Algorithms for Semidefinite Programming (1996)

Venue: | Journal of Optimization Theory and Applications |

Citations: | 19 - 7 self |

### Citations

543 | Interior point methods in semidefinite programming with applications to combinatorial optimization
- Alizadeh
- 1995
(Show Context)
Citation Context ...thematics, University of Iowa, Iowa City, IA 52242, USA. 1 Introduction Many primal-dual interior-point algorithms have been proposed recently for solving semidefinite programming (SDP) problems (cf. =-=[1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15]-=-). Most of these algorithms use one of the following three search directions: the Kojima-Shindoh-Hara direction [6], the Alizadeh-Haeberly-Overton direction [1] and the Nesterov-Todd direction [10]. U... |

252 | An interior-point method for semidefinite programming
- Helmberg, Rendl, et al.
- 1996
(Show Context)
Citation Context ...thematics, University of Iowa, Iowa City, IA 52242, USA. 1 Introduction Many primal-dual interior-point algorithms have been proposed recently for solving semidefinite programming (SDP) problems (cf. =-=[1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15]-=-). Most of these algorithms use one of the following three search directions: the Kojima-Shindoh-Hara direction [6], the Alizadeh-Haeberly-Overton direction [1] and the Nesterov-Todd direction [10]. U... |

214 | A primal-dual interior point algorithm for linear programming
- Kojima, Mizuno, et al.
- 1987
(Show Context)
Citation Context ...rithm In a recent paper [12], we proposed an infeasible-interior-point algorithm for solving (2.3), which generalizes the interior--point method for linear programming proposed by Mizuno, Todd and Ye =-=[8]. The algorithm performs-=- in a neighborhood of the infeasible central path: C(��) = fZ = (X; y; S) 2 S n ++ \Theta IR m \Theta S n ++ : XS = ��I; R i = (��=�� 0 )R 0 i ; i = 1; : : : ; m; R d = (��=�� ... |

203 | Primal-dual interior-point methods for self-scaled cones
- E, Todd
- 1998
(Show Context)
Citation Context ...thematics, University of Iowa, Iowa City, IA 52242, USA. 1 Introduction Many primal-dual interior-point algorithms have been proposed recently for solving semidefinite programming (SDP) problems (cf. =-=[1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15]-=-). Most of these algorithms use one of the following three search directions: the Kojima-Shindoh-Hara direction [6], the Alizadeh-Haeberly-Overton direction [1] and the Nesterov-Todd direction [10]. U... |

164 | Primal-dual path-following algorithms for semidefinite programming
- Monteiro
- 1997
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70 |
S.: Interior point methods for the monotone linear complementarity problem in symmetric matrices
- Kojima, Shindoh, et al.
- 1997
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58 | R.: A superlinearly convergent primal-dual infeasible-interior-point algorithm for semidefinite programming
- Potra, Sheng
- 1998
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56 | M.: Local convergence of predictor-corrector infeasible interior-point algorithm for SDPs and SDLCPs
- Kojima, Shida, et al.
- 1998
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56 | Symmetric primal-dual path following algorithms for semidefinite programming - Sturm, Zhang - 1999 |

54 | Superlinear convergence of a symmetric primal-dual path following algorithm for semidefinite programming
- Luo, Sturm, et al.
- 1996
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47 | On extending primal-dual interior-point algorithms from linear programming to semidefinite programming
- Zhang
- 1998
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35 | Homogeneous interior-point algorithms for semidefinite programming
- Potra, Sheng
- 1995
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34 | A predictor-corrector interior-point algorithms for the semidefinite linear complementarity problem using the Alizadeh-Haeberly-Overton search direction
- Kojima, Shida, et al.
- 1996
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16 |
Positive definite programming
- Vandenberghe, Boyd
- 1994
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11 | Local convergence of predictor-corrector infeasible-interiorpoint algorithms for SDPs and SDLCPs
- M, Shindoh
- 1998
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