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

Franklin, Joel N.

Brossura

ISBN 10: 0898715091 ISBN 13: 9780898715095

Casa editrice: Society for Industrial and Applied Mathematics, 1987

Riassunto

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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Descrizione del libro

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.

Contenuti

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.

Dettagli dell?edizione

• Editore: Society for Industrial and Applied Mathematics
• Data di pubblicazione: 1987
• ISBN 10: 0898715091
• ISBN 13: 9780898715095
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 315