Mathematical View of Interior-Point Methods in Convex Optimization

Name: Mathematical View of Interior-Point Methods in Convex Optimization
Availability: OutOfStock
ISBN: 9780898715026

ISBN-10: 0898715024

ISBN-13: 9780898715026

Edition: 2001

Authors: James Renegar

List price: $64.00

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Description:

This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential…

Book details

List price: $64.00
Copyright year: 2001
Publisher: Society for Industrial and Applied Mathematics
Publication date: 10/31/2001
Binding: Paperback
Pages: 123
Size: 6.75" wide x 9.75" long x 0.50" tall
Weight: 0.550
Language: English



Preface



Preliminaries



Linear Algebra



Gradients



Hessians



Convexity



Fundamental Theorems of Calculus



Newton's Method



Basic Interior-Point Method Theory



Intrinsic Inner Products



Self-Concordant Functionals



Introduction



Self-Concordancy and Newton's Method



Other Properties



Barrier Functionals



Introduction



Analytic Centers



Optimal Barrier Functionals



Other Properties



Logarithmic Homogeneity



Primal Algorithms



Introduction



The Barrier Method



The Long-Step Barrier Method



A Predictor-Corrector Method



Matters of Definition



Conic Programming and Duality



Conic Programming



Classical Duality Theory



The Conjugate Functional



Duality of the Central Paths



Self-Scaled (or Symmetric) Cones



Introduction



An Important Remark on Notation



Scaling Points



Gradients and Norms



A Useful Theorem



The Nesterov--Todd Directions



Primal-Dual Path-Following Methods



Measures of Proximity



An Algorithm



Another Algorithm



A Primal-Dual Potential-Reduction Method



The Potential Function



The Algorithm



The Analysis


Bibliography


Index