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Full Description
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.
Contents
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.
