Separable Optimization: Theory and Methods

The theory, methods, and applications of separable optimization are explored in this book, including approximating separable problems by linear programming, dynamic programming, and convex separable programs with inequality/equality constraints and variable bounds. It also discusses the numerical approximation of tabulated functions, overdetermined systems of linear algebraic equations, and systems of nonlinear equations. The Knapsack polytope is studied, and a new edition includes three new chapters, appendices, and technical details. The book is intended for researchers, practitioners, and engineers interested in separable programming and its applications, particularly in optimization theory, optimization methods, and artificial intelligence and machine learning.

Format: Paperback / softback
Length: 356 pages
Publication date: 27 November 2022
Publisher: Springer Nature Switzerland AG

This comprehensive book delves into the theory, methods, and applications of separable optimization, presenting a wealth of information and insights. It begins by exploring the fundamental concepts and principles of separable optimization, including the definition of separable problems, the necessary conditions for their solvability, and the techniques for approximating them using linear programming and dynamic programming. The book also examines convex separable programs, which are subject to inequality/equality constraints and bounds on variables, and proposes convergent iterative algorithms of polynomial complexity for their solution.

In an application-oriented approach, the algorithms developed are applied to the implementation of stochastic quasigradient methods for solving separable stochastic programs. Furthermore, the book addresses the numerical approximation of tabulated functions, the numerical solution of overdetermined systems of linear algebraic equations, and some systems of nonlinear equations through separable convex unconstrained minimization problems. Additionally, the Knapsack polytope is studied, shedding light on its properties and applications.

The second edition of this book has been extensively revised and updated, incorporating a substantial amount of new and revised content. Three new chapters, 15-17, have been added, providing in-depth analysis of the Knapsack problem and the analysis of a nonlinear transportation problem. Three new Appendices (E-G) have also been included, offering technical details that further enhance the coverage of the subject matter.

Optimization problems and methods have wide-ranging applications in various fields of science, including optimization theory, optimization methods, and their applications. This book, in particular, holds significance from the perspective of artificial intelligence and machine learning within computer science. It serves as a valuable resource for researchers, practitioners, and engineers interested in delving into the detailed treatment of separable programming and leveraging the latest advancements in the field.

In conclusion, this book is a comprehensive and authoritative guide to separable optimization, offering a wealth of knowledge and techniques for solving optimization problems. Whether you are a researcher, practitioner, or engineer, this book will provide you with the necessary tools and insights to excel in your field.

Weight: 575g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030784034
Edition number: 2nd ed. 2021