凹関数解析の基礎と応用 Elements of Concave Analysis and Applications

著者名：Kythe, Prem K.

Chapman and Hall/CRC（2018/05/15発売）

• 言語：ENG
• ISBN：9781138705289
• eISBN：9781351784504

Description

Concave analysis deals mainly with concave and quasi-concave functions, although convex and quasi-convex functions are considered because of their mutual inherent relationship. The aim of Elements of Concave Analysis and Applications is to provide a basic and self‐contained introduction to concepts and detailed study of concave and convex functions. It is written in the style of a textbook, designed for courses in mathematical economics, finance, and manufacturing design. The suggested prerequisites are multivariate calculus, ordinary and elementary PDEs, and elementary probability theory.

Table of Contents

Preface

1 Matrix Algebra

2 Differential Calculus

3 Concave and Convex Functions

4 Concave Programming

5 Convex Programming

6 Quasi-Concave Functions

7 Quasi-Convex Functions

8 Log-concave Functions

9 Quadratic Programming

10 Optimal Control Theory

11 Demands

12 Black-Scholes Equation

Appendices:

A Probability Topics

B Differentiation of Operators

C Distributions

D Laplace Transforms

E Implicit Function Theorem

F Locally Nonsatiated Function