Mathematical optimization and economic analysis
type: Item
instance of: scholarly article
title: Mathematical optimization and economic analysis
zbMATH Open document ID: 1178.90004
DOI: 10.1007/978-0-387-89552-9
published in: Springer Optimization and Its Applications
publication date: 2009-11-30T00:00:00Z
review text: The book is intended to offer the reader a systematic exposition of both single- and multiobjective optimization and their application possibilities in economics. The book is divided into two parts. Part I (Chapters 1--6) is devoted to optimization problems with one objective function, while Part II (Capters 7--9) investigates problems with several objective functions. In Part I, Chapter 1 has an introductory character and contains examples of economic problems, which can be solved using optimization methods. Chapters 2--4 are devoted to the theoretical background of convex and linear programming. Theoretical results are accompanied with motivating examples showing some economic applications. Chapter 5 presents basic DEA (Data Envelopment Analysis) models with applications to technical and environmental efficiency analysis. Chapter 6 is devoted to the theory of geometric programming including an appropriate duality results, and presents economic models, which are foimulated using geometric programming. It is shown how some optimization problems can be transformed into standard geometrical programming models. In Part II, Chapter 7 presents fundamental results of multiobjective optimization, in which several optimality criteria have to be taken into account. Next Chapter 8 studies multiobjective linear programming, i.e. problems, in which both objective functions and constraint functions are linear. Duality theory for such problems is presented and application to Leontiev multiobjective pollution model is described. The last Chapter 9 investigates multiobjective geometric programming, duality theory for multiobjective geometric programming in parametric form, and presents selected applications to environmental control and analysis of monopolist behaviour with two objectives. The book is written in a self-contained form and is intended as a textbook for graduate and postgraduate students studying quantitative economics. It can be of interest also to researchers oriente…
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90-02
Mathematics Subject Classification ID: 90Cxx
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90-01
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5640282
zbMATH Keywords: mathematical optimization
zbMATH Keywords: data envelopment analysis
zbMATH Keywords: geometric programming
zbMATH Keywords: multiobjective optimization
author: Mikulas Luptacik
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-0-387-89552-9
OpenAlex ID: W591765605
description: scientific article; zbMATH DE number 5640282