A mathematical view of interior-point methods in convex optimization /
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| Author / Creator: | Renegar, James, 1955- |
|---|---|
| Imprint: | Philadelphia, PA : Society for Industrial and Applied Mathematics : Mathematical Programming Society, 2001. |
| Description: | vii, 117 p. ; 26 cm. |
| Language: | English |
| Series: | MPS-SIAM series on optimization |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4563539 |
Table of Contents:
- Preface
- 1. Preliminaries
- 1.1. Linear Algebra
- 1.2. Gradients
- 1.3. Hessians
- 1.4. Convexity
- 1.5. Fundamental Theorems of Calculus
- 1.6. Newton's Method
- 2. Basic Interior-Point Method Theory
- 2.1. Intrinsic Inner Products
- 2.2. Self-Concordant Functionals
- 2.2.1. Introduction
- 2.2.2. Self-Concordancy and Newton's Method
- 2.2.3. Other Properties
- 2.3. Barrier Functionals
- 2.3.1. Introduction
- 2.3.2. Analytic Centers
- 2.3.3. Optimal Barrier Functionals
- 2.3.4. Other Properties
- 2.3.5. Logarithmic Homogeneity
- 2.4. Primal Algorithms
- 2.4.1. Introduction
- 2.4.2. The Barrier Method
- 2.4.3. The Long-Step Barrier Method
- 2.4.4. A Predictor-Corrector Method
- 2.5. Matters of Definition
- 3. Conic Programming and Duality
- 3.1. Conic Programming
- 3.2. Classical Duality Theory
- 3.3. The Conjugate Functional
- 3.4. Duality of the Central Paths
- 3.5. Self-Scaled (or Symmetric) Cones
- 3.5.1. Introduction
- 3.5.2. An Important Remark on Notation
- 3.5.3. Scaling Points
- 3.5.4. Gradients and Norms
- 3.5.5. A Useful Theorem
- 3.6. The Nesterov--Todd Directions
- 3.7. Primal-Dual Path-Following Methods
- 3.7.1. Measures of Proximity
- 3.7.2. An Algorithm
- 3.7.3. Another Algorithm
- 3.8. A Primal-Dual Potential-Reduction Method
- 3.8.1. The Potential Function
- 3.8.2. The Algorithm
- 3.8.3. The Analysis
- Bibliography
- Index
