Convexity

Recently I enjoyed surfing homepages of famous people in the control field. At first, I don't even know those people have a homepage. I came across their homepages because I wanted to find an old paper whose electronical version was not available through school's library. So I used google to search the paper's information. And found some authors place pdf files of the papers in their homepage, which is a nice idea from my point of view. I also found there are many interesting things in their homepages, e.g. their lecture notes, old papers, books, biography...

I especially like to see their lecture notes, because they are usually written in a compact way, only the main and important concepts are listed in the notes and tedious calculation are omitted. This helps me to quickly catch the most important idea that the authors want to convey.

Today I read three different people's lecture notes:

1. Stephen P. Boyd: Convex Optimization in Electrical Engineering.
2. Carsten W. Scherer: LMI Relaxations in Robust Control.
3. M. C. de Oliveira: Background material on convexity.

I found one thing in common: they all have the following quote

The greatest watershed in optimiztion is not between linearity and nonlinearity, but between convexity and nonconvexity.

Rockafellar