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Methods of Mathematical Economics

Methods of Mathematical Economics
Linear and Nonlinear Programming, Fixed-Point Theorems

$67.00 (P)

Part of Classics in Applied Mathematics

  • Date Published: January 1987
  • 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

$ 67.00 (P)
Paperback

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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 1987
    • 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.

  • Author

    Joel N. Franklin, California Institute of Technology

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