ABSTRACT

Convexity is an ancient idea going back to Archimedes. Used sporadically in the mathematical literature over the centuries, today it is a flourishing area of research and a mathematical subject in its own right. Convexity is used in optimization theory, functional analysis, complex analysis, and other parts of mathematics.Convex Analysis introduces

chapter 0|2 pages

Why Convexity?

chapter 1|18 pages

Basic Ideas

chapter 3|20 pages

More on Functions

chapter 4|14 pages

Applications of the Idea of Convexity

chapter 5|42 pages

More Sophisticated Ideas

chapter 6|6 pages

The MiniMax Theorem

chapter 7|2 pages

Concluding Remarks