A mathematical view of interior-point methods in convex optimization

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A mathematical view of interior-point methods in convex optimization / James Renegar

資料種別:: 図書
出版情報:: Philadelphia, PA : SIAM
Philadelphia, PA : MPS, 2001
形態:: vii, 117 p. ; 26 cm
シリーズ名:: MPS-SIAM series on optimization <BA49337614>
著者名:: Renegar, James
ISBN:: 9780898715026 [0898715024]
書誌ID:: BA56754382

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注記:

Includes bibliographical reference(p.115-116) and index

主題:

Mathematical optimization

言語:

英語

目次情報:

Preface

Preliminaries / 1：

Linear Algebra / 1.1：

Gradients / 1.2：

Hessians / 1.3：

Convexity / 1.4：

Fundamental Theorems of Calculus / 1.5：

Newton's Method / 1.6：

Basic Interior-Point Method Theory / 2：

Intrinsic Inner Products / 2.1：

Self-Concordant Functionals / 2.2：

Introduction / 2.2.1：

Self-Concordancy and Newton's Method / 2.2.2：

Other Properties / 2.2.3：

Barrier Functionals / 2.3：

Analytic Centers / 2.3.1：

Optimal Barrier Functionals / 2.3.3：

Logarithmic Homogeneity / 2.3.4：

Primal Algorithms / 2.4：

The Barrier Method / 2.4.1：

The Long-Step Barrier Method / 2.4.3：

A Predictor-Corrector Method / 2.4.4：

Matters of Definition / 2.5：

Conic Programming and Duality / 3：

Conic Programming / 3.1：

Classical Duality Theory / 3.2：

The Conjugate Functional / 3.3：

Duality of the Central Paths / 3.4：

Self-Scaled (or Symmetric) Cones / 3.5：

An Important Remark on Notation / 3.5.1：

Scaling Points / 3.5.3：

Gradients and Norms / 3.5.4：

A Useful Theorem / 3.5.5：

The Nesterov--Todd Directions / 3.6：

Primal-Dual Path-Following Methods / 3.7：

Measures of Proximity / 3.7.1：

An Algorithm / 3.7.2：

Another Algorithm / 3.7.3：

A Primal-Dual Potential-Reduction Method / 3.8：

The Potential Function / 3.8.1：

The Algorithm / 3.8.2：

The Analysis / 3.8.3：

Bibliography

Index

Preface

Preliminaries / 1：

Linear Algebra / 1.1：

Gradients / 1.2：

Hessians / 1.3：

Convexity / 1.4：

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