Noniterative Coordination in Multilevel Systems: Nonconvex Optimization and Its Applications

Multilevel systems are ubiquitous in a wide range of applications, from power systems and transportation networks to manufacturing and supply chains. In these systems, multiple decision-makers interact with each other at different levels of a hierarchy to achieve a common goal. Coordination among these decision-makers is essential for the efficient and reliable operation of the system.

However, coordination in multilevel systems can be challenging due to the inherent complexity of these systems. The decision-makers may have different objectives and constraints, and the interactions between them may be nonlinear and nonconvex. This makes it difficult to design coordination mechanisms that are both efficient and robust.

Noniterative Coordination in Multilevel Systems (Nonconvex Optimization and Its Applications, 34)

by Todor Stoilov

4.5 out of 5

Language	:	English
File size	:	1220 KB
Text-to-Speech	:	Enabled
Enhanced typesetting	:	Enabled
Print length	:	108 pages
Screen Reader	:	Supported
Hardcover	:	284 pages
Item Weight	:	1.32 pounds
Dimensions	:	6.14 x 0.69 x 9.21 inches

FREE

In recent years, there has been growing interest in using nonconvex optimization techniques to address the challenges of coordination in multilevel systems. Nonconvex optimization is a powerful tool for solving problems that are difficult or impossible to solve using traditional convex optimization techniques. It can be used to find global optimal solutions to problems with nonlinear and nonconvex objective functions and constraints.

This book provides a comprehensive treatment of noniterative coordination in multilevel systems, with a focus on nonconvex optimization and its applications. It presents a novel approach to the design and analysis of multilevel systems that leverages nonconvex optimization techniques to achieve efficient and robust coordination.

The Foundations of Nonconvex Optimization

The first part of the book provides a foundation in nonconvex optimization. It covers the basic concepts of nonconvex optimization, including:

- The definition of a nonconvex set - The definition of a nonconvex function - The properties of nonconvex functions - The challenges of solving nonconvex optimization problems

The book also discusses the different types of nonconvex optimization algorithms and their convergence properties.

Nonconvex Optimization Algorithms for Multilevel Systems

The second part of the book presents a number of nonconvex optimization algorithms for multilevel systems. These algorithms are designed to solve the coordination problems that arise in multilevel systems, such as:

- The problem of finding a Nash equilibrium - The problem of finding a Pareto optimal solution - The problem of finding a Stackelberg equilibrium

The book discusses the convergence properties of these algorithms and their performance in different types of multilevel systems.

Applications of Nonconvex Optimization in Multilevel Systems

The third part of the book presents a number of applications of nonconvex optimization in multilevel systems. These applications include:

- The design of distributed resource allocation algorithms for power systems - The design of congestion control algorithms for transportation networks - The design of scheduling algorithms for manufacturing systems - The design of supply chain management algorithms

The book discusses the benefits of using nonconvex optimization techniques to solve these problems and the challenges that remain.

Case Studies of Nonconvex Optimization in Multilevel Systems

The fourth part of the book presents a number of case studies of nonconvex optimization in multilevel systems. These case studies illustrate the practical applications of nonconvex optimization techniques in a variety of different settings.

The book concludes with a discussion of the future directions of research in noniterative coordination in multilevel systems.

This book provides a comprehensive treatment of noniterative coordination in multilevel systems, with a focus on nonconvex optimization and its applications. It presents a novel approach to the design and analysis of multilevel systems that leverages nonconvex optimization techniques to achieve efficient and robust coordination. The book is essential reading for researchers and practitioners working in the field of multilevel systems. It is also a valuable resource for students studying multilevel systems, optimization, and control theory.

Noniterative Coordination in Multilevel Systems (Nonconvex Optimization and Its Applications, 34)

by Todor Stoilov

4.5 out of 5

Language	:	English
File size	:	1220 KB
Text-to-Speech	:	Enabled
Enhanced typesetting	:	Enabled
Print length	:	108 pages
Screen Reader	:	Supported
Hardcover	:	284 pages
Item Weight	:	1.32 pounds
Dimensions	:	6.14 x 0.69 x 9.21 inches

FREE