Generalized Concavity (new edition)

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“Generalized Concavity” (new edition), by Mordecai Avriel, Walter E. Diewert, Siegfried Schaible and Israel Zang, book series “SIAM Classics in Applied Mathematics”, vol.63, 329 pp., 2010, ISBN 978-0-89871-896-6, eISBN 978-0-89871-943-7, DOI

Table of Contents

  • Preface to the Classics Edition
  • Preface
  1. Introduction
  2. Concavity
    2.1. Basic Definitions
    2.2. Single-Variable Concave Functions
    2.3. Concave Functions of Several Variables
    2.4. Extrema of Concave Functions
    2.5. Concave Mathematical Programs
  3. Generalized Concavity
    3.1. Quasiconcave Functions–Definitions and General Properties
    3.2. Differentiable Quasiconcave Functions
    3.3. Strict Quasiconcavity
    3.4. Semistrict Quasiconcavity
    3.5. Pseudoconcave Functions
    3.6. Generalized Concave Mathematical Programs
  4. Application of Generalized Concavity to Economics
    4.1. The Cost Function
    4.2. Duality between Cost and Production Functions
    4.3. Generalized Concavity and Producer Theory
    4.4. The Consumer’s Utility Maximization Problem
    4.5. Semistrict Quasiconcavity and Consumer Theory
    4.6. Strict Quasiconcavity and Consumer Theory
    4.7. Strong Pseudoconcavity and Consumer Theory
    4.8. Pseudoconcavity and Consumer Theory
    4.9. Profit Maximization and Comparative Statics Analysis
    4.10. Concave Programs and Economics
  5. Special Functional Forms I: Composite Functions, Products, and Ratios
    5.1. Composite Functions
    5.2. Products and Ratios
  6. Special Functional Forms II: Quadratic Functions
    6.1. Main Characterization of Quasiconcave, Pseudoconcave, and Strictly Pseudoconcave Quadratic Functions
    6.2. Characterizations in Terms of an Augmented Hessian
    6.3. Characterizations in Terms of the Bordered Hessian
    6.4. Strictly Quasiconcave and Strongly Pseudoconcave Quadratic Functions
    6.5. Quadratic Functions of Nonnegative Variables
  7. Fractional Programming
    7.1. Notation and Dennitions
    7.2. Applications
    7.3. Concave Fractional Programs
    7.4. Algorithms in Concave Fractional Programming
  8. Concave Transformable Functions
    8.1. Concave Transformable Functions: Range Transformation
    8.2. Conditions for Concavifiability of Twice Continuously Differentiable (C2) Functions
    8.3. Concave Transformable Functions: Domain and Range Transformations
  9. Additional Generalizations of Concavity
    9.1. F-Concave Functions
    9.2. Generalized Arcwise Connected Functions
  • Supplementary Bibliography
  • Author Index
  • Subject Index