MA5630
NUMERICAL OPTIMIZATION
SPRING 2003

Instructor information

• Instructor: Mark S. Gockenbach, PhD
• Office: 309 Fisher
• Office phone: 487-3083
• Email: msgocken@mtu.edu
• Office hours: MWF 2-3pm and by appointment

Note: I am available to help students whenever I am in my office; please feel free to drop by. However, I usually work at home in the morning, so you are unlikely to find me on campus before 11am.

Course information

• Class meets MWF 11:05-11:55 pm in 327B Fisher for lecture and discussion.
• Text: Numerical Optimization by Nocedal and Wright (Springer, 1999).
• Course homepage: http://www.math.mtu.edu/~msgocken/ma5630spring2003

Lectures

Problem Sets

Course description

Numerical optimization is the study of algorithms for solving optimization problems. We will study problems that can be posed as nonlinear programming (NLP) problems:

$$\begin{eqnarray*}\min&f(x)\\ s.t.&g(x)=0\\ &h(x)\ge 0. \end{eqnarray*}$$

Here $f:{\bf {\rm R}}^n\rightarrow{\bf {\rm R}}$, $g:{\bf {\rm R}}^n\rightarrow{\bf {\rm R}}^m$, and $h:\rightarrow{\bf {\rm R}}^p$, that is, each of the functions f, g, and h depend on n variables. The scalar-valued function f is the objective function, and the vector-valued functions g and h define the constraints on the variables. We will study algorithms that are applicable to problems with hundreds to perhaps a few thousand variables, and also spend some time discussing algorithms that can be applied to problems with many thousand variables.

Because the general NLP is quite difficult, we will study special cases of increasing difficulty:

• unconstrained optimization:
  
  $$\min f(x)$$
  
  

• equality-constrained NLP:
  
  $$\begin{eqnarray*}\min&f(x)\\ s.t.&g(x)=0\\ \end{eqnarray*}$$
  
  
• inequality-constrained NLP:
  
  $$\begin{eqnarray*}\min&f(x)\\ s.t.&h(x)\ge 0\\ \end{eqnarray*}$$
  
  

In addition to studying the algorithms themselves, we will cover the theory that is necessary for designing and analyzing the algorithms.

Grading

Course grades will be based on 4 problem sets, a take-home midterm exam, and a take-home final exam, weighted as follows:

Problem sets (4)	200 points
Midterm	100 points
Final	100
Total	400 points

The grading scale for each assignment will be announced when the graded assignment is returned.

Assignments will generally have both theoretical and computational problems (requiring programming), and students will be able to choose which aspect they want to emphasize. In this way, the course should be accessible and interesting to both mathematics and engineering students.