First-order methods in optimization

著者

• Beck, Amir

書誌事項

First-order methods in optimization

Amir Beck

（MOS-SIAM series on optimization, 25）

Society for Industrial and Applied Mathematics : Mathematical Optimization Society, c2017

注記

Includes bibliographical references (p. 457-472) and index

内容説明・目次

内容説明

The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.

目次

• Preface
• Chapter 1: Vector Spaces
• Chapter 2: Extended Real-Value Functions
• Chapter 3: Subgradients
• Chapter 4: Conjugate Functions
• Chapter 5: Smoothness and Strong Convexity
• Chapter 6: The Proximal Operator
• Chapter 7: Spectral Functions
• Chapter 8: Primal and Dual Projected Subgradient Methods
• Chapter 9: Mirror Descent
• Chapter 10: The Proximal Gradient Method
• Chapter 11: The Block Proximal Gradient Method
• Chapter 12: Dual-Based Proximal Gradient Methods
• Chapter 13: The Generalized Conditional Gradient Method
• Chapter 14: Alternating Minimization
• Chapter 15: ADMM
• Appendix A: Strong Duality and Optimality Conditions
• Appendix B: Tables
• Appendix C: Symbols and Notation
• Appendix D: Bibliographic Notes
• Bibliography
• Index.

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詳細情報

• NII書誌ID(NCID): BB25312536
• ISBN:
  • 9781611974980
• LCCN: 2017026859
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Philadelphia
• ページ数/冊数: xii, 475 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA402.5
  • DC23 : 519.6
• 件名:
  • LCSH : Mathematical optimization
  • LCSH : Convergence
• 親書誌ID:
  • BB09877431