Large-Scale Convex Optimization : Algorithms & Analyses via Monotone Operators

This introduction to the theory of convex optimization algorithms presents a unified analysis of first-order optimization methods using the abstraction of monotone operators. The text empowers graduate students in mathematics, computer science, and engineering to choose and design the splitting methods best suited for a given problem.

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.