Basics of optimization: Chap. 1, 2.
Line Search Methods: Chap. 3.1-3.3 (pp. 30-47).
Trust-Region Methods: Chap. 4.1, 4.3 (pp. 66-77 and 83-92).
Conjugate Gradient Methods: Chap. 5.
Quasi-Newton Methods: Chap. 6.1, 6.4 without SR1 method (pp. 135-143, 153-160).
Least-Squares Problems: Chap. 10.1-10.3 without large-residual problems (pp. 245-262).
Constrained Optimization: Chap. 12.1-12.5 without projected Hessians (pp. 304-336).
Linear Programming: Chap. 13.1-13.2, 14.1 (pp. 355-366, 392-406).
Quadratic Programming: Chap. 16.6 (pp. 480-485).
Penalty Methods: Chap. 17.1-17.3 (pp. 497-519).
Sequential Quadratic Programming: Chap. 18.1, 18.2, parts of 18.3 (merit functions), 18.4 (pp. 529-535, 540-543, 545-546).