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First-Order Methods In Optimization

Amir Beck (author)

ISBN: 9781611974980

Publication Date: Nov 2017

Format: Paperback

Provides a self-contained, comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. 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.
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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.
Pages 484
Dimensions 229 x 152
Date Published 30 Nov 2017
Publisher SIAM - Society for Industrial and Applied Mathematics
Series MOS-SIAM Series on Optimization
Series Part 25
Subject/s Applied mathematics   Computer science  
  • 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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