Numerical Optimization: Lecture Notes

This is a set of lecture notes for MATH 555, Penn State's graduate Numerical Optimization course. Numerical Optimization is the study of maximizing or minimizing functions through numerical techniques. Generally, it's rare to optimize anything other than through numerical techniques (unless of course you're talking about something really simple). Numerical optimization is used every day and is built on techniques from multi-variable calculus, optimization theory (obviously) numerical linear algebra (for algorithm efficiency) and other branches of mathematics.

The lecture notes are loosely based on Nocedal and Wright's book Numerical Optimization, Avriel's text on Nonlinear Optimization, Bazaraa, Sherali and Shetty's book on Non-linear Programming, Bazaraa, Jarvis and Sherali's book on Linear Programming and several other books. All of the books mentioned are good books (some great). The problem is, some books don't cover things in enough depth. The other problem is for students taking this course, this may be the first time they're seeing optimization, so we have to cover some preliminaries. This set of notes correct some of the problems I mention by presenting the material in a format for that can be used easily in Penn State in MATH 555. These notes are probably really inappropriate if you have a strong Operations Research program. You'd be better off reading Nocedal and Wright's book directly.

In order to use these notes successfully, you should know something about multi-variable calculus. It also wouldn't hurt to have had an undergraduate treatment in optimization (in some form).