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Generalized Concavity Click on picture to view full-size image Generalized Concavity

Mordecai Avriel, Walter E. Diewert, Siegfried Schaible, and Israel Zang

Classics in Applied Mathematics 63

Originally published in 1988, this enduring text remains the most comprehensive book on generalized convexity and concavity. The authors present generalized concave functions in a unified framework, exploring them primarily from the domains of optimization and economics.
Concavity of a function is a common property used in most of the important theorems concerning properties of optimization problems in mathematical economics, operations research, mathematical programming, engineering, and management science. Generalized concavity deals with the many nonconcave functions that have properties similar to those of concave functions.
Specific topics covered in this book include:a review of concavity and the basics of generalized concavity; applications of generalized concavity to economics; special function forms such as composite forms, products, ratios, and quadratic functions; fractional programming; and concave transformable functions.

Mathematicians, economists, computational mathematicians, management scientists, operations researchers, and optimization theorists will find this book useful.

Preface to the Classics Edition;
Chapter 1: Introduction;
Chapter 2: Concavity;
Chapter 3: Generalized Concavity;
Chapter 4: Application of Generalized Concavity to Economics;
Chapter 5: Special Functional Forms I: Composite Functions, Products, and Ratios;
Chapter 6: Special Functional Forms II: Quadratic Functions;
Chapter 7: Fractional Programming;
Chapter 8: Concave Transformable Functions;
Chapter 9: Additional Generalizations of Concavity;
Supplementary Bibliography;
Author Index;
Subject Index.

About the Authors
Mordecai Avriel is Director of Analytical Development at Bank Hapoalim in Tel Aviv, Israel, and is Professor Emeritus of the Faculty of Industrial Engineering and Management at Technion—Israel Institute of Technology.
Walter E. Diewert is Professor of Economics at the University of British Columbia.
Siegfried Schaible is Chair Professor in the Department of Applied Mathematics at Chung Yuan Christian University, Chung-Li, Taiwan. He has published a great deal of original research in both generalized convexity and generalized monotonicity, and in 1996 he founded the international Working Group on Generalized Convexity (
Israel Zang is President of the Academic College of Tel-Aviv-Yaffo and a Professor Emeritus of the Recanati Faculty of Management at Tel Aviv University.

2010 / xvi + 332 pages / Softcover / ISBN 978-0-898718-96-6
List price $77.50 / SIAM Member Price $54.25 / Order Code CL63
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Banner art adapted from a figure by Hinke M. Osinga and Bernd Krauskopf (University of Auckland, NZ.)