Generalized concavity

✍ Scribed by Avriel M., et al.

• Publisher: SIAM
• Year: 2010
• Tongue: English
• Leaves: 346
• Series: Classics in Applied Mathematics
• Category: Library

✦ Synopsis

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. Audience: Mathematicians, economists, computational mathematicians, management scientists, operations researchers, and optimization theorists will find this book useful. Contents: Preface to the Classics Edition; Preface; 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.

✦ Table of Contents

Contents......Page 8
Preface to the Classics Edition......Page 10
Preface......Page 13
1 Introduction......Page 15
2 Concavity......Page 29
3 Generalized Concavity......Page 69
4 Application of GeneralizedConcavity to Economics......Page 115
5 Special Functional Forms I:Composite Functions,Products, and Ratios......Page 167
6 \rSpecial Functional Forms II:Quadratic Functions......Page 181
7 \rFractional Programming......Page 221
8 Concave Transformable \rFunctions......Page 245
9 Additional Generalizations of \rConcavity......Page 307
10 Supplementary Bibliography......Page 335
Author Index......Page 339
Subject Index......Page 343