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9781611974980 Academic Inspection Copy

First-Order Methods in Optimization

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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.
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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