Mathematical optimization and economic analysis
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 oriented to applications of mathematical models in economics.
scientific article; zbMATH DE number 5640282