Methods of Mathematical Economics
Linear and Nonlinear Programming, Fixed-Point Theorems
£44.99
Part of Classics in Applied Mathematics
- Author: Joel N. Franklin, California Institute of Technology
- Date Published: January 2003
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
- format: Paperback
- isbn: 9780898715095
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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 fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker 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.
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×Product details
- Date Published: January 2003
- format: Paperback
- isbn: 9780898715095
- length: 315 pages
- dimensions: 227 x 154 x 16 mm
- weight: 0.439kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface to the Classics Edition
Preface
Errata
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
Zero-Sum, Two-Person Games
Integer Programming. Gomory's Method
Network Flows
Assignment and Shortest-Route Problems
The Transportation Problem
2. Nonlinear Programming. Wolfe's Method for Quadratic Programming
Kuhn-Tucker Theory
Geometric Programming
3. Fixed-Point Theorems. Introduction to Fixed Points
Contraction Mappings
Garsia's Proof of the Brouwer Fixed-Point Theorem
Milnor's Proof of the Brouwer Fixed-Point Theorem
Barycentric Coordinates, Sperner's Lemma, and an Elementary Proof of the Brouwer Fixed-Point Theorem
The Schauder Fixed-Point Theorem
Kakutani's Fixed-Point Theorem and Nash's Theorem for n-Person Games
Index.
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