Mathematical View of Interior-Point Methods in Convex Optimization
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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 elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $39.50
Copyright year: 2001
Publisher: Society for Industrial and Applied Mathematics
Size: 6.75" wide x 9.75" long x 0.50" tall
|Fundamental Theorems of Calculus|
|Basic Interior-Point Method Theory|
|Intrinsic Inner Products|
|Self-Concordancy and Newton's Method|
|Optimal Barrier Functionals|
|The Barrier Method|
|The Long-Step Barrier Method|
|A Predictor-Corrector Method|
|Matters of Definition|
|Conic Programming and Duality|
|Classical Duality Theory|
|The Conjugate Functional|
|Duality of the Central Paths|
|Self-Scaled (or Symmetric) Cones|
|An Important Remark on Notation|
|Gradients and Norms|
|A Useful Theorem|
|The Nesterov--Todd Directions|
|Primal-Dual Path-Following Methods|
|Measures of Proximity|
|A Primal-Dual Potential-Reduction Method|
|The Potential Function|