Optimal control theory. Applications to management science and economics
type: Item
instance of: scholarly article
title: Optimal control theory. Applications to management science and economics
zbMATH Open document ID: 1487.49001
DOI: 10.1007/978-3-030-91745-6
author: Suresh P. Sethi
published in: Springer Texts in Business and Economics
publication date: 2022-01-03T00:00:00Z
review text: The author of this book is an expert in operations management, finance and economics, marketing, optimization, optimal control, etc. The first two editions of the book [Optimal control theory. Applications to management science. Boston/The Hague/London: Martinus Nijhoff Publishing (1981; Zbl 0495.49001); Optimal control theory. Applications to management science and economics. 2nd ed. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0998.49002); Optimal control theory. Applications to management science and economics. 3rd edition. Cham: Springer (2019; Zbl 1412.49001)] were published by the same author in cooperation with \textit{G. L. Thompson}, and naturally the present fourth edition includes the contributions of both experts. We also point out that the material of this book has been discussed with students, since its level allows to do so. Obviously, the book is primarily addressed to students and researchers in management science, operations research, and economics. The book comprises 13 chapters, 5 appendices, a long reference list, and an index (plus lists of figures and tables). Chapter 1 (entitled ``What is Optimal Control Theory?'') comprises 5 sections: 1.1 Basic Concepts and Definitions; 1.2 Formulation of Simple Control Models; 1.3 History of Optimal Control Theory; 1.4 Notation and Concepts Used; 1.5 Plan of the Book. In addition, at the end of Chapter 1 there are appropriate exercises and a specific reference list. Chapter 2 (``The Maximum Principle: Continuous Time'') introduces the maximum principle as a necessary condition that must be satisfied by any optimal control for the basic problem formulated in Section 2.1 of this chapter. Specifically, the state equation considered here is an ODE in the Euclidean space \(E^n\), \[ \dot{x}(t)=f(x(t),u(t),t), \ t\in [0,T], \ \ x(0)=x_0, \] where \(u(t) \in E^m\) is the control variable. The admissible controls are assumed to be piecewise continuous functions \(u\) satisfying a constraint of the form \(u(t)\…
Mathematics Subject Classification ID: 49-01
Mathematics Subject Classification ID: 91-01
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N10
Mathematics Subject Classification ID: 49S05
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 91B76
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 90B30
Mathematics Subject Classification ID: 90B60
Mathematics Subject Classification ID: 91A23
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 7451851
zbMATH Keywords: optimal control theory
zbMATH Keywords: management science
zbMATH Keywords: finance
zbMATH Keywords: production
zbMATH Keywords: inventory
zbMATH Keywords: marketing
zbMATH Keywords: natural resources
zbMATH Keywords: economics
zbMATH Keywords: maximum principle
zbMATH Keywords: differential games
zbMATH Keywords: stochastic optimal control
zbMATH Keywords: Markov diffusion process
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-030-91745-6
OpenAlex ID: W4205776077
description: scientific article; zbMATH DE number 7451851