Large-Scale Convex Optimization

Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods - including parallel-distributed algorithms - through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.

Preface; 1. Introduction and preliminaries; Part I. Monotone Operator Methods: 2. Monotone operators and base splitting schemes; 3. Primal-dual splitting methods; 4. Parallel computing; 5. Randomized coordinate update methods; 6. Asynchronous coordinate update methods; Part II. Additional Topics: 7. Stochastic optimization; 8. ADMM-type methods; 9. Duality in splitting methods; 10. Maximality and monotone operator theory; 11. Distributed and decentralized optimization; 12. Acceleration; 13. Scaled relative graphs; Appendices; References; Index.