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Lectures on Convex Optimization

  • Yurii Nesterov

Part of the Springer Optimization and Its Applications book series (SOIA, volume 137)

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Black-Box Optimization

    1. Front Matter
      Pages 1-1
    2. Yurii Nesterov
      Pages 3-58
    3. Yurii Nesterov
      Pages 59-137
    4. Yurii Nesterov
      Pages 139-240
    5. Yurii Nesterov
      Pages 241-322
  3. Structural Optimization

    1. Front Matter
      Pages 323-323
    2. Yurii Nesterov
      Pages 325-421
    3. Yurii Nesterov
      Pages 423-487
    4. Yurii Nesterov
      Pages 489-570
  4. Back Matter
    Pages 571-589

About this book

Introduction

This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning.

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 find this 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.

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

Authors and affiliations

  • Yurii Nesterov
    • 1
  1. 1.CORE/INMACatholic University of LouvainLouvain-la-NeuveBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-91578-4
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-91577-7
  • Online ISBN 978-3-319-91578-4
  • Series Print ISSN 1931-6828
  • Series Online ISSN 1931-6836
  • Buy this book on publisher's site
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