Overview
- Presents a self-contained description of fast gradient methods
- Offers the first description in the monographic literature of the modern second-order methods based on cubic regularization
- Provides a comprehensive treatment of the smoothing technique
- Develops a new theory of optimization in relative scale
Part of the book series: Springer Optimization and Its Applications (SOIA, volume 137)
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Table of contents (7 chapters)
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Front Matter
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Black-Box Optimization
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Front Matter
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Structural Optimization
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Front Matter
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Back Matter
Keywords
- complexity
- complexity theory
- graphs
- mathematical programming
- optimization
- Fast Gradient Methods
- Self-Concordant Functions
- Interior-Point Methods
- Smoothing Technique
- Cubic Regularization of Newton Method
- Optimization in Relative Scale
- MSC 2010 49M15, 49M29, 49N15, 65K05, 65K10, 90C25, 90C30, 90C46
- 90C51, 90C52, 90C60
- algorithm analysis and problem complexity
About this book
Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail.
Researchers in theoretical optimization as well as professionals working on optimization problems will findthis book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.Reviews
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Lectures on Convex Optimization
Authors: Yurii Nesterov
Series Title: Springer Optimization and Its Applications
DOI: https://doi.org/10.1007/978-3-319-91578-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-91577-7Published: 01 December 2018
eBook ISBN: 978-3-319-91578-4Published: 19 November 2018
Series ISSN: 1931-6828
Series E-ISSN: 1931-6836
Edition Number: 2
Number of Pages: XXIII, 589
Number of Illustrations: 1 b/w illustrations
Topics: Optimization, Algorithm Analysis and Problem Complexity, Algorithms