## ECE/Math 520: Nonlinear Programming (Spring 2012)

### Prof. Dan Bates (math), TR 9:30-11, Engineering E205

Optimization is a beautiful and extremely applicable field of mathematics and engineering. There are myriad applications throughout engineering, the sciences, and business. The basic idea is that you want to make some choice (how many of each product to produce, for example) given some constraints (you only have so much capital, there is a limited supply of raw materials, you cannot have negative quantities, etc.) so as to maximize or minimize some function (revenue, cost, time, etc.). Applications range from very small, easy problems (think ma and pa bait shops) to massive, seemingly intractable problems (airplane scheduling, NetFlix, etc.).

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).

### Homework

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).

### Talk schedule

• Tuesday, 4/10: Tegan Emerson: Primal-Dual Interior Point Method
• Tuesday, 4/17: Mark Oxley: A Tabu Search Approach to Optimization of Resource Allocation in Heterogeneous Computing
• Thursday, 4/19:
• LATE START (10 am)
• Yehan Long: Mixed Integer Programming, applied to Fire Risk and Fuel Treatment Evaluation
• Tuesday, 4/24:
• Ryan Friese: Using Genetic Algorithms to Solve Bi-Objective Optimization Problems
• Tim Hansen: Using Genetic Algorithms to Allocate Resources to Applications
• Thursday, 4/26: Yishai Statter: Optimization in VLSI Electronic Design Automation
• Tuesday, 5/1:
• Eric Hanson: Optimization as a tool in Numerical Algebraic Geometry
• Tim Marrinan: Comparing Subspace Mean Algorithms

Several other people are kicking around ideas. If you have any thoughts or want me to suggest some options, just let me know!

### Examples

Simple steepest descent example: Maple (*.mw), pdf.