Modern Optimization Methods for Decision Making Under Risk and Uncertainty

Synopsis

The book comprises original articles on topical issues of risk theory, rational decision making, statistical decisions, and control of stochastic systems. The articles are the outcome of a series international projects involving the leading scholars in the field of modern stochastic optimization and decision making. The structure of stochastic optimization solvers is described. The solvers in general implement stochastic quasi-gradient methods for optimization and identification of complex nonlinear models. These models constitute an important methodology for finding optimal decisions under risk and uncertainty. While a large part of current approaches towards optimization under uncertainty stems from linear programming (LP) and often results in large LPs of special structure, stochastic quasi-gradient methods confront nonlinearities directly without need of linearization. This makes them an appropriate tool for solving complex nonlinear problems, concurrent optimization and simulation models, and equilibrium situations of different types, for instance, Nash or Stackelberg equilibrium situations. The solver finds the equilibrium solution when the optimization model describes the system with several actors. The solver is parallelizable, performing several simulation threads in parallel. It is capable of solving stochastic optimization problems, finding stochastic Nash equilibria, and of composite stochastic bilevel problems where each level may require the solution of stochastic optimization problem or finding Nash equilibrium. Several complex examples with applications to water resources management, energy markets, pricing of services on social networks are provided. In the case of power system, regulator makes decision on the final expansion plan, considering the strategic behavior of regulated companies and coordinating the interests of different economic entities. Such a plan can be an equilibrium − a planned decision where a company cannot increase its expected gain unilaterally.

Copyright:

2024

Book Details

Book Quality:

Publisher Quality

Book Size:

380 Pages

ISBN-13:

9781000983968

Related ISBNs:

9781032196411, 9781003260196, 9781032196435

Publisher:

CRC Press

Date of Addition:

10/06/23

Copyrighted By:

Alexei A. Gaivoronski, Pavel S. Knopov and Volodymyr A. Zaslavskyi

Adult content:

No

Language:

English

Has Image Descriptions:

No

Categories:

Nonfiction, Computers and Internet, Mathematics and Statistics

Submitted By:

Bookshare Staff

Usage Restrictions:

This is a copyrighted book.

Edited by:

Alexei A. Gaivoronski

Edited by:

Pavlo S. Knopov

Edited by:

Volodymyr A. Zaslavskyi