Convex Analysis

 Outline: (copied from here)

The course is a foundational overview of convex analysis. It begins by studying real valued convex functions of one real variable and some of their properties including continuity, and closedness. It then studies convex sets, with particular emphasis on the indicator functions of these convex sets. It generalizes the earlier exposition to study convex functions of several variables. The second half of the course focuses on duality and conjugate functions. Throughout the course, geometry will be stressed and plenty of examples will be worked out to clarify concepts.  A brief outline of the course follows:

Other useful resources:

Exercises:

For those who are eager to do more exercises, there is a textbook that can meet your appetite:

Convex Analysis and Optimization, Dimitri P. Bertsekas, Athena Scientific.

The solution of all exercises is available here.

As for original exercises, download the scanned copy here by chapter:       

        ch 1 (13 pages, 45 questions)   2    3    4    5    6    7    8

More notes:

Sometimes, the book says "obviously", "it is easy to see...".  Well, sometimes it is not easy to understand it in an obvious way.  So I will write down the steps as memo.

Counter-examples:

Here I will collect all the interesting counter-examples, which is a very important aspect of learning analysis.

Definitions:

I will put all the definitions together in one file, for easy reference.  A lot of new terminologies!

Theorems and important properties:

I will put all the important theorems, lemmas, corollaries, propositions together in one file, for easy reference.