
2002 / xviii + 297 pages / Softcover / ISBN: 9780898715095 / List Price $58.00 / SIAM Member Price $40.60 / Order Code CL37
Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixedpoint theorems. In this easytoread classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the KuhnTucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences.
The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely. By providing the necessary proofs and presenting the material in a conversational style, Franklin made Methods of Mathematical Economics extremely popular among students. The addition of a list of errata, new to this edition, should add to the book's popularity as well as its usefulness both in the classroom and for individual study.
The book has three chapters: "Linear Programming," "Nonlinear Programming," and "FixedPoint Theorems." The first and third chapters include the economic equilibrium theorems of von Neumann and of J. F. Nash, while the second chapter includes KuhnTucker theory and Wolfe's simplex algorithm for quadratic programming. The book concludes with easy, elementary proofs of the famous theorems of Brouwer, of Kakutani, and of Schauder. These fundamental results are usually proved only in advanced texts in topology, economic theory, and nonlinear analysis.
Audience
This book is intended for undergraduate and graduate students of mathematics and economics; it requires no background in these areas except an understanding of elementary calculus and linear algebra.
Contents
Preface to the Classics Edition; Preface; Errata; Chapter 1: Linear Programming. Introduction to Linear Programming; Linear Programs and Their Duals; How the Dual Indicates Optimality; Basic Solutions; The Idea of the Simplex Methods; Separating Planes for Convex Sets; Finite Cones and the Farkas Alternative; The Duality Principle; Perturbations and Parametric Programming; The Simplex Tableau Algorithm; The Revised Simplex Algorithm; A Simplex Algorithm for Degenerate Problems; Multiobjective Linear Programming; ZeroSum, TwoPerson Games; Integer Programming: Gomory's Method; Network Flows; Assignment and ShortestRoute Problems; The Transportation Problem; Chapter 2: Nonlinear Programming. Wolfe's Method for Quadratic Programming; KuhnTucker Theory; Geometric Programming; Chapter 3: FixedPoint Theorems. Introduction to Fixed Points; Contraction Mappings; Garsia's Proof of the Brouwer FixedPoint Theorem; Milnor's Proof of the Brouwer FixedPoint Theorem; Barycentric Coordinates, Sperner's Lemma, and an Elementary Proof of the Brouwer FixedPoint Theorem; The Schauder FixedPoint Theorem; Kakutani's FixedPoint Theorem and Nash's Theorem for nPerson Games; Index.
ISBN: 9780898715095