Modern Optimization Methods for Decision Making Under Risk and Uncertainty

The book discusses the structure of stochastic optimization solvers and their application to solving complex nonlinear problems, concurrent optimization, and simulation models. It also provides examples with applications to water resources management, energy markets, and pricing of services on social networks.

Format: Hardback
Length: 380 pages
Publication date: 06 October 2023
Publisher: Taylor & Francis Ltd

The book is a comprehensive resource that delves into various aspects of risk theory, rational decision-making, statistical decisions, and the control of stochastic systems. It comprises a collection of original articles authored by renowned scholars in the field of modern stochastic optimization and decision-making. These articles result from extensive international projects involving top experts in the area.

The book begins by providing an in-depth exploration of the structure of stochastic optimization solvers. These solvers are designed to implement stochastic quasi-gradient methods for optimization and identification of complex nonlinear models. These models play a crucial role in finding optimal decisions under risk and uncertainty. While traditional approaches to optimization under uncertainty often rely on linear programming (LP) and result in large LPs with specific structures, stochastic quasi-gradient methods directly address nonlinearities without the need for linearization. This makes them highly effective tools for solving complex nonlinear problems, concurrent optimization and simulation models, and equilibrium situations of various types, such as Nash or Stackelberg equilibrium situations.

One of the key features of stochastic optimization solvers is their ability to find the equilibrium solution when the optimization model describes a system with multiple actors. The solver is designed to be parallelizable, allowing for the simultaneous execution of multiple simulation threads. This enables it to handle large-scale stochastic optimization problems efficiently. Furthermore, the solver is capable of solving stochastic Nash equilibria, as well as composite stochastic bilevel problems where each level may require the solution of a stochastic optimization problem or finding a Nash equilibrium.

To illustrate the practical applications of stochastic optimization, the book includes several complex examples with applications to water resources management, energy markets, pricing of services on social networks, and power systems. In the case of power systems, regulators make decisions on the final expansion plan, considering various strategic factors. By leveraging stochastic optimization techniques, regulators can optimize the allocation of resources and minimize the risk of system failures.

Overall, the book serves as a valuable resource for researchers, practitioners, and students interested in the field of risk theory, rational decision-making, statistical decisions, and the control of stochastic systems. It provides a comprehensive overview of the latest developments and techniques in stochastic optimization, making it an essential tool for anyone seeking to advance their knowledge and expertise in this area.

Weight: 880g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032196411