- Convex functions are defined on p. 67
- The conjugate is defined on p. 91 (Note that there are at least three distinct uses of the term "conjugate" in mathematics. As far as I know, this one is distinct from the "conjugate" in "conjugate gradient methods".)
- Convex optimization problems are defined in Sections 4.1 and 4.2
- Duality is the subject of Chapter 5. The function to be optimized is modified by adding the constraints multiplied by quantities called Lagrange multipliers. If an equality constraint is satisfied, this doesn't change the value being optimized. If an inequality constraint is satisfied, this improves the value being optimized. This is similar to the notion of adding a regularizer to the function being optimized. I plan to cover at least Sections 5.1 and 5.2 and probably the KKT conditions on p. 243
- Interior-point methods are discussed in Chapter 11. We'll see how far we get. In any case it's worth reading the bibliographic notes on p. 621