## Interior-point polynomial algorithms in convex programming |

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### Contents

Selfconcordant functions and Newton method | 11 |

Pathfollowing interiorpoint methods | 57 |

Potential reduction interiorpoint methods | 101 |

Copyright | |

8 other sections not shown

### Other editions - View all

Interior Point Polynomial Algorithms in Convex Programming Yurii Nesterov,Arkadii Nemirovskii Limited preview - 1987 |

Interior-point Polynomial Algorithms in Convex Programming Yurii Nesterov,Arkadii Nemirovskii Limited preview - 1994 |

Interior Point Polynomial Algorithms in Convex Programming Yurii Nesterov,Arkadii Nemirovskii No preview available - 1987 |

### Common terms and phrases

absolute constant affine mapping arithmetic cost Assume assumptions barrier F barrier for G barrier method belongs bounded CA(E closed convex domain compute concordant barrier conic problem conic representation convergence convex cone convex function convex optimization convex programming convex representation convex set corresponding defined definition denote dual ellipsoid epigraph equation feasible set follows functional element gradient homogeneous self-concordant barrier implies int G interior-point methods intersects intG intG+ iteration latter inequality latter relation Legendre transformation Lemma let F Let G Let us prove Let us verify linear linear programming linear subspace main stage matrix minimize monotone element monotone operator nonempty interior nonnegative norm Note optimal value parameter path-following method positive-semidefinite preliminary stage primal Proof Proposition quadratic form self-concordant function semidefinite programming solvable solve standard step strictly feasible solution strongly self-concordant subspace suffices symmetric symmetric matrix Theorem updating variational inequality vector virtue