\(\def\Real{\mathbb{R}}\)

Convex programming and duality: Guler, Chapter 11.

Class notes (pretty incomplete, to be used just as a study guide), here and here.

**Exercises**:

Find Legendre duals for the following functions:

- \(f(x)=\min(1-x,2,1+x)\);
- \(f(x)=\min((x-1)^2,(x+1)^2)\);
- \(f(x,y)= 0 \mathrm{\ if\ } x^2+y^2\leq 2; +\infty \mathrm{\ otherwise}\).

## No comments yet.