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

This text provides a unified analysis of first-order optimization methods, including parallel-distributed algorithms, through the abstraction of monotone operators. It is designed for graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science, and covers the construction and analysis of classical and modern algorithms using monotone operators.

Format: Hardback
Length: 400 pages
Publication date: 01 December 2022
Publisher: Cambridge University Press

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.

In recent years, there has been a significant increase in the demand for efficient optimization algorithms that can handle large-scale problems. This has led to the development of various techniques, such as convex optimization, which are specifically designed to solve complex optimization problems efficiently. Convex optimization is a branch of mathematics that deals with the study of optimization problems in which the objective function is convex, meaning that it is a combination of non-negative linear functions. The main advantage of convex optimization is that it can be solved using a variety of methods, including linear programming, nonlinear programming, and dynamic programming. One of the most important applications of convex optimization is in the field of machine learning. Machine learning is a branch of computer science that involves the use of algorithms to learn from data. In machine learning, the objective is to find the best possible model that can predict the outcome of a given problem. Convex optimization is used to optimize the parameters of machine learning models, such as the weights and biases of neural networks, to improve their performance. Another application of convex optimization is in the field of finance. In finance, the objective is to maximize the return on investment while minimizing the risk. Convex optimization is used to optimize the portfolio of investments, such as stocks and bonds, to achieve this objective. In addition to these applications, convex optimization is also used in a wide range of other fields, such as engineering, logistics, and operations research. For example, convex optimization is used to design efficient production plans, optimize transportation routes, and solve complex scheduling problems. Overall, convex optimization is a powerful tool that has a wide range of applications in various fields. Its ability to solve complex optimization problems efficiently has made it a popular choice among researchers and practitioners alike. As the demand for optimization algorithms continues to grow, it is likely that convex optimization will continue to play an important role in developing new and innovative solutions to complex problems.

Weight: 790g
Dimension: 186 x 263 x 26 (mm)
ISBN-13: 9781009160858