## Problem Complexity and Method Efficiency in Optimization |

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### Contents

CONVEX PROGRAMMING | 42 |

METHODS OF MIRROR DESCENT | 83 |

COMPLEXITY OF CLASSES | 125 |

Copyright | |

7 other sections not shown

### Common terms and phrases

absolute constant absolute error affine functionals approximate solution assertion asymptotic ball Banach space centre class of problems co-ordinates complexity consider constructed convergence convex function convex problems convex programming corresponding defined definition denote depend deterministic methods deterministic oracle domain ensure estimate extremal problems field of problems first-order oracle fo(x function f given gradient method Hahn–Banach theorem Hilbert space inequality int G laboriousness lemma let f Let G linear Lipschitz Lipschitz-convex problems lower bound MD-methods measure method described method of solving minimizing MMCG modulus of strong noise norm obtained optimization parameters point xe Polish space possible problem f proof properties prove question regarded relative error required accuracy satisfied smooth solving games solving problems stochastic programming sufficiently support functional Suppose theorem trajectory unit ball upper bound values vector weak topology x e G xe G ye G