ABSTRACT

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.

chapter 1|28 pages

Matrix Algebra

chapter 2|34 pages

Differential Calculus

chapter 3|24 pages

Concave and Convex Functions

chapter 4|34 pages

Concave Programming

chapter 5|32 pages

Convex Programming

chapter 6|26 pages

Quasi-Concave Functions

chapter 7|18 pages

Quasi-Convex Functions

chapter 8|20 pages

Log-Concave Functions

chapter 9|16 pages

Quadratic Programming

chapter 10|18 pages

Optimal Control Theory

chapter 11|20 pages

Demands

chapter 12|34 pages

Black-Scholes Model