There is a fundamental split in optimization between linear and nonlinear problems. This course will focus on the theory, algorithms, and applications on the nonlinear side, though we will touch on the linear side a bit. I won't assume you know anything about linear programming for this course.
Prof. Edwin Chong (over in ECE) usually teaches this course, and he has built a very nice course. As a result, I will largely follow his plan for covering the material. We will also be using Chong's book. For a lot more details, please check out his website. As I said, I will cover much of the ground that is usually covered in this course, though I might emphasize things a little differently (no big changes).
Edwin Chong's Math/ECE 520 webpage
HW 1 (due Tuesday, 2/7): Please do 3.8, 5.8, 5.9a, 6.1, and 6.7 AND any FIVE of 2.1, 2.7, 3.7, 3.12, 3.14, 3.15, 3.18ab, 6.3, 6.6, and 6.9-20.
HW 2 (due Thursday, 3/1): 7.2, 9.3, 9.4, and any four of the following: 7.3b, 7.3c, 7.7, 7.8ab, 7.9, 8.3, 8.5, 8.15, 8.19, 8.20, 8.24, 8.25, 10.9, and 10.10. Feel free to use software other than Matlab! No need to send the code; please just provide sample input and output.
HW 3 (due Thursday, 3/29): Please do any EIGHT of the following (noticing that a few count as 2 problems!): 11.7, 11.8, 11.13, 11.14, 11.15, 14.2 (counts as 2), 14.3 (counts as 2), 14.4 (counts as 2), 14.5, 14.11 (counts as 2), 19.1a, 19.1b, 19.2, 19.3, 19.4, 19.6ab, 19.7, 19.12, 20.1b, 20.3, 20.4ab, 20.5a, 20.6a.
HW 4 (due Thursday, 5/3): Please do any SIX of the following: 12.1-12.7 (each counts as one; do no more than 2 of these as they are so similar), 14.2 (counts as 2), 14.3 (counts as 2), 14.11 (counts as 2), 15.4-10 (each counts as one), 16.2-4 (each counts as one), 16.8, 16.13, 16.16a, 16.18 (counts as 3).
Several other people are kicking around ideas. If you have any thoughts or want me to suggest some options, just let me know!
Simple steepest descent example: Maple (*.mw), pdf.