Chapter 2
Theorem 2.2 (w/o proof)
Definition 2.4
Knowledge of simple RK methods (Euler, trapezoidal)
Definition of order
Lemma 2.5 (proof)
Lemma 2.6 (proof)
Concept of autonomization and Lemma 2.7 (w/o proof)
Rooted trees
Theorem 2.12 (w/o proof)
Theorem 2.16 (proof idea)
Chapter 3
Theorems 3.2 + 3.3 (w/o proof)
Absolute stability, stability domain
Definition 3.7
Theorem 3.8 (w/o proof)
Lemma 3.9 (proof)
Algorithm (3.16)
Examples of implicit RK (implicit Euler, implicit midpoint rule)
Why are Rosenbrock methods important?
Chapter 4
Theorem 4.1 (proof)
Theorem 4.2 (proof)
Theorem 4.3 (w/o proof)
Understand the gaps between necessity and sufficiency for second-order conditions
descent direction
Armijo rule (4.5)
Lemma 4.6 (w/o proof)
Algorithm 4.7
Theorem 4.11 (w/o proof)
Theorem 4.12 (first part of proof, 1. and 2.)
Theorem 4.13 (w/o proof)
BFGS
Idea of nonlinear CG (Algorithm 4.16)
Definition 4.18
Lemma 4.19 (proof)
Definition 4.21
Lemma 4.22 (idea of proof)
Idea of Algorithm 4.24
Theorem 4.26 (w/o proof)
Algorithm 4.28
Theorem 4.29 (w/o proof)
Chapter 5
Definition 5.4
Theorem 5.5 (proof)
Definition 5.8
Theorem 5.11 (precise statement + full proof, w/o proof of Farkas)
Theorem 5.12 (w/o proof)
Solution of QP (5.21)
Lemma 5.13 (w/o proof)
Algorithm 5.1
Idea of IP methods; derivation of (5.31)
Definition 5.16
Theorem 5.17 (proof)
Lemma 5.20 1, 4, + (5.45) (w/o proof)
Lemma 5.21 (proof)
(5.49) + optimal choice of alpha for strongly convex, smooth f