Optimization, MA 348
Kurt Bryan, Spring 2006
What Is Optimization?
Optimization is about finding the "best" answer to a given
question, for example:
- What's the optimal mix of stocks, bonds and
cash for a given investment objective?
- Where should a new
manufacturing plant be located in order to minimize distribution
costs?
- What trajectory will get a probe from Earth to Mars orbit
using the least amount of fuel?
Check out this link
for a ton of example applications. Optimization is an extension of
the min/max ideas developed in first-year calculus. It's one of
the hottest areas in applied mathematics, with applications
ranging from oil exploration to designing new drugs. I've used
optimization techniques in many real applications.
Prerequisites
The only prerequisites for this course are:
- The first year calculus sequence and DE I (but you really don't even need the
DE);
- A desire to use mathematics to solve some real problems.
General Course Description
Since the first step in any optimization problem is describing the
situation mathematically, this course includes a healthy dose of
modeling. The solution of the problem typically involves the application of
a numerical optimization algorithm, so we'll spend a lot of time looking
at various approaches. The actual computations will be carried out in either
Matlab or Maple, using "canned" routines. You don't need to know anything
deep about Maple or Matlab for this course.
The grading in this course will be based on homework assignments,
in-class work, and a couple of take-home exams. You'll also have the chance
to apply what you learn on the last homework, in which you can find
or formulate an optimization problem which interests you (maybe from your major
area, maybe not!), then solve it. Some past problems included
- Finding the least expensive diet which meets the U.S. RDA for
various vitamins and minerals.
- Finding the best variables for predicting future stock
prices.
- Determining the values of unknown electrical components in a
circuit, by taking only external measurements.